For instance, several versions of Firefox had a serious bug in shared workers, which appeared intermittently when users opened your site in multiple tabs https://stackoverflow.com/questions/51092596/feature-detecti... - I had to use the user agent to work around this.
Bundling into adblockers or browsers directly would help.
Chrome could change its header to the header of a competitor or a neural one, but has no reason to (Google's main business is delivering ads). For other big browsers like Firefox and Safari it would be a huge loss to change the header: they would vanish from browser market share statistics, and with that the business case to make websites work well with their browser dwindles. That in turn would reduce their actual market share. That only leaves the browser with a market share so tiny they are ignored by developers, and those browsers do often spoof the user agent header (or at least make it very convenient to do so).