Up the tourist path? Have you been up there yourself? Not really, it's a long series of zig zags and generally good underfoot, you could easily walk it in brogues[1]. It's not having enough layers if the weather came in that would kill people up there, or losing the path on the summit and not having map/compass or the skill to find it again in a whiteout, then ending up on the Carn Mor Dearg Arete (or worse one of the rock climbs) which are an entirely different game and quite dangerous for the ill-equipped and ill-trained.
Snowdon would be similar, as long as it hadn't snowed the Llanberis path would be fine in trainers, but stray onto Crib Goch and you are not unlikely to die (and I'm not overstating that).
There is a certain "thou shalt have dry feet and ankle support" prejudice in the hillwalking community, which does carry some weight but as someone who is also an occasional fell-runner there is a totally different view on kit there, and in any case my fell-running shoes are actually far grippier than my hiking boots, so on very poor ground, wet feet aside, I'd probably rather be in those! And they just look like a pair of regular trainers other than the brand.
[1] Which might be seen as a formal shoe these days but are actually the traditional Scottish country walking shoe for rich landowners!