Not all browsers, but Chrome certainly desires to be fingerprintable. They even try to cryptographically prove that the current browser is an unmodified Chrome with Web Environment Integrity [1].

Doesn't get more fingerprintable than that. They provide an un-falsifiable certificate that "the current browser is an unmodified Chrome build, running on an unmodified Android phone with secure boot".

If they didn't want to fingerprintable, they could just not do that and spend all the engineering time and money on something else.

[1]: https://en.wikipedia.org/wiki/Web_Environment_Integrity