In continental EU, I already get stuff from Mouser Italy, and in pretty much same time frame as Farnell.
Farnell also opened large warehouse in France, and might start serving continental EU from there more and more.
As for TI and Avnet, I think it might be something else. Just few days ago I received email from TI that I can buy directly from TI Europe..
Even small quantities.. They also offer company credit lines...
So they might be trying to not having a need for distributors at all, or at least much less....