Thing is, every time they do that, it taxes their resources; more game modes potentially mean 1) more "special" balancing for those game modes / maps that require individual attention, 2) adding/removing/banning/tweaking items for said modes, 3) listening to the rage and anger of people whining about how unbalanced the game mode is, and 4) having to consider those games modes, even if only to a minor extent, when creating Champions - "Will this completely break X game mode"
Small correction in that, yes, more game modes do tax Riot's resources, but mainly in terms of bug fixes. Crashing doesn't reflect well on Riot's product, so those bugs, like the recent Sion one, are fixed relatively quickly. Non-crashing bugs are lower priority and take a while to patch, like the "Azir leaves the fountain early" bug that was around for a few patches.
Balance changes for the alternate maps, whether item or champion, are rare. URF got about as many changes in one patch as TT and Dom combined got in years. (Skimming over patch notes since the start of 2015, it looks like there's been one champion change, a TT mini-rework, Mark/Dash added to ARAM, and about ten item changes to sync up with SR item changes.) Furthermore, alternate maps aren't typically considered when Riot makes new champs. Look at all the collection mini-games Riot's been adding in (Bard, GP, Garen) or the fact that Azir still has no passive at all on Dominion.
Basically, the main impact of more game modes is that Riot needs to do that much more bug testing to make sure nothing crashes League. Balance concerns are an afterthought at most.