You definitely could. Though apparently in incognito mode it's recommended that browsers just throw an exception rather than provide fake data: https://github.com/WICG/floc/blob/dcd4c042fa6a81b048e04a78b1...

Throwing an exception in incognito mode allows websites to detect incognito mode, which is not desirable. Incognito mode should provide fake data.

Google have stated that they are not interested in preventing fingerprinting.

Of course the FLoC team would want browsers to throw an exception, since that wouldn't damage the perceived legitimacy of FLoC. But as a user I'd rather feed them false data if possible.

There are quite a few ways for a site to distinguish private/incognito from normal browsing, and IMO these differences should be treated as bugs. Indeed, these differences often break sites (including a vaccine registration site) that should work fine. We don't need even more ways for sites to break in private/incognito mode.

Totally agree, browsers should strive to make it so websites cannot tell if users are browsing privately or not.

Sure, but you would have to be careful with that though, if you use any Google services they might ban your account with no recourse.

Could that be a blessing in disguise.