Right.

: Is 'benefit' really the right word to use for fragile meatsacks like us? = )

We're different from other non-humanoid biological beings for multiple reasons, not just our legs and humanoid torso. What if another factor is that having a humanoid machine manned by a human creates a total that's more than the sum of its part? Subconsciously it could be a more natural structure environment (this gets into sci-fi territory of training and 'becoming one' with the machine ala Pacific Rim). ie, would a human controlling (as if his own body) a non-humanoid vehicle fair better or worse than if an actual humanoid mech? *shrug*
Remember we're discussion future fictional sci-fi mechanical constructs :P it's all in theory.

: That said, a lot of the reasons I hear for why mechs are so good comes down
: to anthropocentric bunk. "Mechs are great because they're made in our
: image, and we are awesome."

Enh, I don't buy that. That argument is highly fallacious. There are many reasons why we as humans fair better than non-humanoid beings. But heck, this argument is more like "is it better to have opposable thumbs or not?" -- both structure have benefits and drawbacks; they're specialized for certain activities and tasks. As humans we obviously have some weaknesses, we're not the optimal form for certain environments or conditions. Yet, we still fair better overall because overcome those drawbacks in other ways.

Are vehicles better in some contexts than mechs? Of course. Can mechs be better in some contexts than vehicles? Of course. It all depends HOW they're designed and/or engineered, and operated. And, who operates them and how optimally. So many factors.

You seem to be coming from an angle that all mechs can be out-done by non-humanoid vehicles. I'm saying only that I think just to make that statement is fallacious. Maybe that's a non-argument that can't go anywhere - I can't provide practical examples, because I'm not an engineer from the future. All examples we have are glorified science fiction/anime artistic concepts that have little to no basis in reality or actual science (as at our currently tech level).

My argument is simply this: Based on the fact that we humans are generally more capable than any other biological being (our state of existence serves to demonstrate that, whatever your ethics about how we live may be), it is more likely that if we design mechs to take advantage of our advantages - whether biological or intellectual or whatever - we will, theoretically, be able to create a mech that given a certain specified purpose, might be able to be more beneficial than non-humanoid vehicles.

Heck even that statement can have issues. Vehicles would be designed with the same thing in mind. A vehicle doesn't have legs and a torso, so given its design, it would be engineered to be optimal as such given its purpose. Just like a mech, with legs and a torso. To label having or not having that attribute as a strength or weakness is already weighed down by an external parameter. Rather, it's simply an attribute that needs to be designed around - whether making use of them as a strength, or considering them as a weakness, in a context.

: Can anybody say what /advantages/ mechs have over vehicles? All I'm getting
: here is a bit of "they can climb over obstacles," which is an
: edge case considering how "All Terrain" conventional vehicles
: can be.

I didn't say that was the only advantage. Nor do I believe that is the only advantage (see above). How do we make use of the unique attributes practically, advantageously? (see above)

: And yes, it's a weakness, and the question is "What are you trading
: off?" By basing your vehicle off a much more limited platform, what
: strengths are you gaining in turn?

Right. Say you're given the task to build (or obtain) a vehicle (mech or not) to accomplish a task. The vehicle design you run would likely be based on analyzing strengths and weaknesses of vehicle classes; sizes, weights, flexibility, usability, durability, etc etc in the context of its mission. Assuming a time when mechs are as feasible (and varied) a vehicle to build (practically speaking) as any other vehicle, then the properties of a mech would also be taken into consideration. Then you may go about customizing the vehicle to see what optimizations you can eek out of the design for its particular specialization.
In a time when mechs are as feasible a vehicle as motorcycles are to garbage trucks today, then yes, a mech would have places where it's more optimal towards a task than other vehicles.

: I'm not a mechspert * either. I'm just an engineer and a hardware junkie who
: is somewhat frustrated by the prevalence of a sci-fi trope.

Don't blame the trope, blame the writers :P
I'm no mechspert either (sorry, it's out there now, gotta use it! :) but I hate blanket matter-of-fact statements about fictional constructs :P

: Another benefit of vehicles: Their natural resting state is right side up, on
: the ground.
: Natural resting state of mechs: Horizontal.

If designed-- sorry, engineered that way. (I hope the spirit of my words was picked up more than the literal meanings :P)

: There was a machine I saw once, made by... John Deere? Can't remember.
: It was a walker. A logging machine with multiple legs and de-
: Fine. I did a google search, and here it is:
: http://www.theoldrobots.com/Walking-Robot2.html

circa... how old was that? No one's disputing that today mech engineering (2, or whatever-legged) leaves much to be desired in comparison to specialized vehicles :)

: So, can we add "crime scene investigation" and "Clearing
: minefields" to the list of jobs mechs might do?

Sure. But I think there will always be purists who say humans can always do everything better :P we have endless great sci-fi that explores that human vs machine dynamic. :) Probably also part of the reason why humans are always the average jack-of-all-trades in fantasy settings :)

: (As another aside, I just had the image of Greenpeace activists trying to
: stop it by hooking a rope to one of the legs and running around and around
: and around and around... until the operator clocks them with the
: harvester.)

I can imagine the look on the operator's face as he watches the activist run around and around...

: I find it hard to sum up the disgust I feel when I look at that image.
: Probably just because I'm trapped in a festering pit of writer's block at
: the moment.

As long as there's no Sarlacc or Rancor in your midst!

: Is the Mantis's role as an anti-aircraft vehicle enhanced in any way by the
: presence of legs?

Dunno. Practically, it could turn on a dime, maybe dodging incoming fire is a benefit (sometimes I really wish I could strafe (faster?) in a vehicle in Halo; I hate being locked in a one on one skirmish in a vehicle vs another highly versatile vehicle, like a Ghost :P) - which, by the way, is an example of a vehicle design that works around a weakness of typical linear motion vehicles. Now is there a tradeoff in using hover vs treads or other non-linear vehicle design? What about legs? There really are far too many factors in vehicular engineering to state "mechs are never better than vehicles" (or something along those lines).

: A forklift with a boom and mechanical hand would work better at my job than a
: Cyclops, because a forklift can roll across a concrete floor with a heavy
: load.
: You can take a Cyclops, add counterweights for whatever load it might carry,
: adjust the gait so that the load doesn't get rocked, etc. But at that
: point, why bother?

*shrug* I'd leave that up to engineers to decide. Do drawbacks of any particular design in its practical context outweigh the benefits?
They made segways work :) (not saying that tech necessarily applies directly here :P just the principle)

: All that said, the Spirit of Fire is NOT my workplace (Alas). Cyclopses may
: be designed to repair vehicles in a mundane motor pool with a flat deck,
: but they might also have to repair the Spirit of Fire after a hard fight.
: Then, the ability to crawl through crumpled bulkheads would speak for
: itself.

Makes me picture the scene from The Core, and wish never to be crushed in a collapsing compartment under high pressure. o_O Also, I don't think any mech suit would have helped him in that context (inside the vessel, inside earth's core)
Also, spoiler? nah