It does not matter much either way. The underlying collision/movement model should work with floating point geometry/math for higher accuracy and be mostly independent from visuals and whole pixels.
True, but you have to be careful here. Some OpenGL games have occasional subpixel gaps between tiles, and AFAICS this is because the texture mapping is fractionally off.
Good point about the centring problem.
There is absolutely no technical reason to restrict yourself to powers of 2 unless you are using ancient hardware.
I don't know if it's a 'technical' reason, more of a 'design' reason, but screen resolutions, and texture resolutions, tend to be divisible by 8 (and also often by 16, 32, and 64). This means that choosing one of those values can guarantee a whole number of tiles fits onscreen. Picking a non-power-of-two makes it very difficult to make such a guarantee. According to the type of gameplay or if you are pushed for texture space, that may matter.
I would agree that picking powers of two for purely 'it goes fast' reasons is specious. Picking a 'unified global sprite size' (as opposed to tile size) in general is specious. Sprites tend to be of all sorts of sizes which is fine, you don't need to make them match tile sizes exactly; But the tiles are sort of like the 'grid' that you are working with to design the entire game, so it -does- warrant careful consideration.
Involving both artist and programmer discussing -actual situations that are planned to come up in game-, not hypothetical 'circles work better' or 'X game uses NxN tiles'. I guess that was a problem I had with the OP.. all design decisions need to have a concrete basis or things get silly.