I think its pure game mechanic, it would seem slightly unfair if you had several different types of forsaken while everyone had only 1 type with slight cosmetic differences, after all a orc is an orc. Anyway Blizzard also tries to make everything balanced (i.e. Trolls don't have a capital so neither does the Gnomes), so if there was different types of forsaken then they'd have to balance the other factions (or have the player base be very unhappy), which at the end of the day means a lot of work on not 'new' content.

Pure game mechanic (thinks like having an additional "body" option instead of the usual cut, color, facial etc.) and probably simply the time and resources needed to actually make those different models (even if they may be variations of the exitings models for other races it might have taken quite a bit of time.

I also think I read something about every race beiing identifiable on spot even from afar to balance the game. Having an undead that could be mistaken for gnome e.g. is not what Bliz wanted.

Finally lorewise I think the excuse for only humans is, that despite the fact that there surely are undead trolls, orcs, elves etc., except for the elite of the Death Knights (the turned warriors) the majority (personal guess 90%) of the forsaken is made up of Lorderon former common folk. Farmers, craftsmen, merchants etc. So the chance of YOU being anything else is simply ignored.

Surely game mechanics played a role, but the Forsaken are specifically the former humans of Lordaeron and the surrounding lands. If there are non-human Forsaken (like the Dark Rangers we see in Undercity now), they must be a tiny minority. There simply weren't that many non-humans living in Lordaeron at the time of the plague.