If you're not set on Mordheim, but want a high-magic fantasy skirmish game, then I recommend looking into Frostgrave.
It's very light on background, so you can use the FG rules to run games that (in your head fluff) are actually taking place in Mordheim, or elsewhere in the Old World. There are no rules for 'races' but that doesn't stop you using elves, skaven, or whatever instead of humans.
I definitely agree with your general point. I'm not sure I quite follow the reference to Frostgrave here. I think one thing that people like about Frostgrave is that, as well as being model-agnostic, it's almost background agnostic. There's so little developed background/lore that you can use the rules while filling in the 'fluff' of your world in all kinds of ways.Diving into the setting for any of these games, including Frostgrave (which is a bit more forced with everyone playing a Wizard searching for “wizard loot”) can really make the difference for it to be a big selling point.