I'd be curious to see a somewhat-objective look at what's actually wrong with default browser styles, separating out well-established usability and design considerations from personal preferences and branding preferences. I wouldn't be at all surprised if there are near-universal things wrong with the default styles, and those might be possible to change if they can be separated out.
Default styles aren’t pretty.
That’s it. They’re superior in every other way. You always know what to click, you always know what an element will do, how it behaves, the UX is consistent with your OS, etc. Default elements are fantastic.
Buttons in Chrome on macOS look completely different than in native apps. Buttons and context menu in Chrome's native <video> controls look yet again different, following Material Design. From the things one could argue are good about native browser styles "consistency with the OS" is definitely not one of them.
Of course, it’s worth putting the effort in to both looking good and working good, but if we’re going to pick one, we should go for the second.
Combo boxes are a fucking nightmare to style, as are checkboxes and radios. Buttons arnt as bad, but you still spend a lot of time fighting against browser defaults which differ across browsers.
Your comment below about being difficult to style is more to the point.