It's possible. But it's a huge undertaking. If you just wanted to fully understand all of the specifications for HTTP, JavaScript and CSS, it'd take you days before having written a single line of code.

Then you need to write all that in a performant way.

Then you need to keep up with all the new features.

Then you need to keep up with all the new security threats.

Browsers nowadays are practically little operating systems. So the question is not that far off from asking what prevents you from writing an alternative to Windows.

You can. But it'll cost millions, or maybe billions, to build something good.