YMMV.
I would say "no". I think the point I disagree with is how the OP frames the content of the PHB in the wider world. It's always been my assumption that adventurers, what the PCs are, are outliers. Unusual. Eberron is a setting that specifically says otherwise, but in most other settings, magic isn't commonplace, ie a part of everyday life for the average person. For example, in most settings, most clergy of a given temple have no caster levels.
But to touch on larger issues, it really depends on what steampunk means. If it i just a checklist of aesthetic elements, then possibly. But steampunk isn't just a "look". It is a narrative genre or subgenre if on wants to really get technical. Is the baseline D&D setting put forward in 5e PHB steampunk thematically? I don't feel so, but I would be happy to hear the case for such.