Would it be possible to serve a fake fingerprint that appears legitimate? Or even better mimic the finger print of real users who've visited a site you own for example?
Yes, that's what web scraping services do (full disclaimer I work at scrapfly.io). Collecting fingerprints and patching the web browser against this fingerprinting is quite a bit of work so most people outsource this to web scraping APIs.
some projects worth checking out: https://github.com/refraction-networking/utls https://github.com/berstend/puppeteer-extra