From the sound of it, there's no appreciable difference in features between MP4 and MKV unless you're planning to use special features like captions or alternate audio tracks, which I assume you aren't. It's mostly used by people who want to make rips of DVDs and Blu-Ray discs and keep all the features intact. Meanwhile, MP4 is supported by default on every player in existence nowadays, whereas MKV only works in VLC, Media Player Classic, and some other, even more obscure stuff that only works on computers and Android.
I can't help but think the descriptions in the poll may have skewed the vote a bit, since there was no mention of MP4's much wider support and everyone on the Internet hates Apple. Plus, that bit about MKV being "open source" is a moot point since H.265 itself is neither open source nor patentless. If this were a debate between MPEG and, say, OGG or WebM, that would be another matter.
Those who need MP4 are the ones least likely to have the slightest clue what "remuxing" even is, much less how to do it. The goal here is accessibility; that's why he's planning on discontinuing the WMV copies in the first place.