As long as the essential controls are there (play/pause, volume, transport) and don't have serious UX sins (tiny or otherwise lacking touch targets) restyling them is overrated.
And an unfortunate number of recreated controls seem to have the serious UX sins.
"looks different in every single browser" is a minor issue. Might be nice if they were restylable via CSS, though.
> <audio controls src="example.mp3"></audio>
> <video controls src="example.mp4"></video>
Which look different in every single browser and can't be styled without JavaScript. Wish these were implemented better.