What's wrong with wanting a site to look like a mockup?

Typically results in custom controls and working against the browser provided affordances

Of course, but I pride myself in able to create custom code and not just rely on some built-in stuff.

The operative piece of the above post (to me) is "working _against_ the browser", not the existence of custom code per se. IME lots of problems with UI development have come (partly) from shoehorning tech to do something it's not meant to do, at the expense of speed, accessibility, and general usability. If the built-in thing doesn't do what you need, by all means build something that does, but it's worth keeping in mind that often the useful thing that end users actually need/want is the built-in thing.

Why do you consider it a good thing to not use standard controls?

Nothing when mockups are iterable and editable by the team and when the designer is part of the team.

A hell of useless code/new APIs/authorization issues just for no customer value but only discutable esthetics considerations when mockups are designed up front by some never available designer like they are some inviolable part of the specifications thus are enforced to the team.