Only feasible with reasonable eletric muscles (muscles that work by contraction rather than rotation by motor) and power supplies. Battletech (and, by connection, Mechwarrior) has a pretty good idea there. They have fusion power, so they generate far more energy than any movement system would require, so power efficiency isn't an obstacle. Second, they have eletric muscles offering greater strength, greater density, and presumably greater robustness: half a muscle has partial efficiency, half a wheel has zero efficiency.
Add to that the increased potential to cover differing terrain and the ability to, with a good interface, more intuitively control the vehicle and I think you have something worthy of consideration.
As for the people talking about things like instability and falling over, that's a problem that bipedal species have evolved a nice way of dealing with: getting back up. Of course the thing is going to be terrible if it doesn't have the maneuverability to get back up when it falls over or the durability to survive such a fall. You're falling into the trap of asking whether a mech is feasible with CURRENT technology. The question is whether the technology that WOULD be required for feasibility is itself feasible, and I think the answer is probably yes. It's likely that we'll develop better sources of portable power, it's likely that they could be used to run even extremely inefficient mechanical muscles, and it's likely that you could achieve the flexibility and control necessary to allow for complex movements like standing up. As for the likelihood that significant research money would ever go that direction in the first place, these are all things that are either independently desirable or desirable in full mech form for a huge variety of professions. Large-scale working bipedal vehicles would be inestimably useful for all sorts of work from construction to farming. The military could then do what it does best: take the idea and turn it into a weapon.