Onno Meyer wrote:

One way is to arbitrarily stack the deck against normal vehicles,
but I don't want to do that. Any power plant or weapon system for
a Mecha should be useable in wheeled, tracked or flying tanks as well, and there should still be a niche for Mecha.

I'd say you have something of a problem then, since stacking the deck is pretty much required. Some general observations, though:

1) You probably want supertech actuators (artificial muscles); while it's possible to build a human-sized walking vehicle with current tech (though it will underperform a human) the required muscle performance scales in a linear manner with height -- if you want a 20' mech, you want actuators with at least 3x the performance of human muscle. 2) The primary flaw of vertical (vs horizontal) designs (walker or otherwise) is that you have a large frontal area relative to your volume. Thus, you want tech assumptions where that doesn't matter -- which probably means a setting dominated by indirect fire (where top area matters more) or other sorts of attacks that come from off angles. Sadly, the weapons mecha are normally portrayed as using are direct fire weapons where a tank-like build is ideal. 3) One way around the shape problem is a setting where shape is almost entirely irrelevant for defensive purposes. This makes sense if the primary defenses used in the setting are not a function of surface area (for example, force fields).

* Superscience TL11+ could allow reactionless vectored thrust
  AFVs with legs rather than skids. But how to explain the arms
  instead of a turret.

Depending on actuator technology, arms aren't necessarily that horrible a choice. However, how do you explain powered legs rather than skids or struts? It's a total waste of mass.
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