Unless something has changed that I missed, you can install extensions (I complained when the default args messed this up [0]). For example, I built something that uses puppeteer and an extension to capture audio and video of a tab [1]. It's just headless mode that doesn't allow extensions [2] (which I now realize is probably what you meant).
0 - https://github.com/GoogleChrome/puppeteer/issues/850 1 - https://github.com/cretz/chrome-screen-rec-poc/tree/master/a... 2 - https://bugs.chromium.org/p/chromium/issues/detail?id=706008
I haven’t looked into it, but I imagine it has a pretty clear fingerprint as well. So it would be easier to block than stock chrome in headless mode.