> Wouldn't more Tor 3rd party integration (soon Brave, Mozilla in the future, ...) lead to greater incentive for website operators to allow Tor?
That seems like a long game. Tor is starting with a minuscule marketshare; Fusion will only be used by users in a special mode, afaict - again, probably very few; and if Brave's marketshare is higher or lower, the difference is immaterial. There are even websites that aren't compatible with Firefox itself, or so I'm told; it will be a long time before anyone cares about Tor users.
Also, users whose personal data is harder to access are less valuable to the website; websites have an incentive to make it harder to use Tor. Finally, many associate Tor with criminality; that's not an attractive market and it's very easy for the CSO to say, 'just block it; it's not worth the time or cost'.