Yes, Google Play does allow you to build free apps without ads. I put them in as a little experiment; I'd never made a mobile app before so I wanted to try things out.As an added bonus it also enabled me to gain back some of the costs I made developing XWC (website template, domain & hosting, iOS developer account, lots of spare time, etc.)
Okay - let's not play patty-cakes about this:
You put in the ads to make some money. The 'little experiment' was, "How much money could this app make back with these ads?" (that said, I'm not judging here - fair enough that you would like to recover costs and/or derive a profit from the work you put into the app).
This is why Disney felt confident delivering a C&D to you and not, say, to Mu0n regarding his Vassal module - once you attach a source of revenue, you're no longer protected by fair use. It's the most concrete part of fair use law: it only applies to not-for-profit endeavors. Without the ad revenue, it would come down to a question of whether or not you could successfully defend the app's educational value in court, and Disney is quite unlikely to want to risk that sort of entanglement (which is why i don't think anyone else running the various ad free list builders should be sweating it).