As Martijn Pieters comment suggests, this already happens in the form of an association bonus.
Quoting from Jeff's answer -
The feature is intended for experienced users who have already reached
this threshold, and are now proceeding to new sites in the network.
That way they aren't "noobs" on the new site, they have 101 rep and
can use all the core functions.
This "association bonus" is also mentioned in the FAQ -
If you are an experienced Stack Exchange network user with 200 or more
reputation on at least one site, you will receive a starting +100
reputation bonus to get you past basic new user restrictions. This
will happen automatically on all current Stack Exchange sites where
you have an account, and on any other Stack Exchange sites at the time
you log in.
To sum things up, as you can see - once you have a certain amount of reputation on one site you are no longer considered a newbie and are awarded 100 rep to bypass all of the newbie limitations like commenting everywhere and down/upvoting. Together with this it should be noted that your expertise in one area does not make you any more competent in another. I am pretty good with programming, hence my 6K+ rep on Stack Overflow. However, I don't have a clue when it comes to apple software, physics, bicycles, wordpress... the list goes on but I'll stop here :P On those sites I am no longer bound by the limitations enforced on new users but my 6K rep means nothing outside of Stack Overflow...