You don’t have to style the select. If you are being forced to, your designers are either incompetent or ignorant. Aesthetics shouldn’t trump usability
It's not that it isn't an extreme position, but I think you are right that many(most?) designers don't appreciate the usability tradeoffs they are requesting in doing so. Most designer I've had this discussion with have come around to not doing styling like this after having the tradeoffs explained to them.
Speaking of design trade-offs, I've found it's really hard to get stakeholders to appreciate the cost of implementing designs. Design cost should be part of the trade-off give-and-take of figuring out what can fit in a release or sprint or whatever, but often all those decisions happen too early in the process to do that. It's easy for one design decision to affect several "stories" and add tens of "points" (in typical agile terminology) to a project, and entirely possible that the stakeholders would rather have five more features than have that widget look and behave just so. Most designers don't seem to consider this much.
That was my initial point actually: a lot of these tradeoffs happen accidentally since for instance you have to write a custom component to do something basic as changing the background color of a select options.
If more powerful browser components would be available then designers would be happy to just style those, and functionality and accessibility would still be fine.
Many designers I have worked with got into UI design from a graphic design/art/print background[1]. Many I have worked with had never read so much as a word from any OS platform's human interface guidelines and were, indeed, ignorant of HCI fundamentals.
[1] graphic design is a completely legitimate field and a good way to get into UI design, but if that's all you've got, you still have quite a way to go
I don't believe there are many designers who are interested in creating experiences with poor usability, thus my point about ignorance and not understanding the tradeoff they are making. On "incompetence", if a designer understands fully that they are creating something that will be less useable and accessible for the sake of aesthetics they have earned the label. To take the HN search page as an example, the filters can't be interacted with via keybord or screen reader. When it's your job to help users solve problems and you have made it knowingly harder to do that, I don't see how that's competent.
Luckily, it has been my experience that in most cases(including my own) the former, rather than the latter, is at play.