TLS 1.0 seem to be vulnerable to Beast, Lucky13 and maybe other attacks and is simply outdated. Common workaround used e.g. by Google was to use RC4 which was also recently broken, but none of the major browsers seem to be implementing newer version of TLS, except Microsoft IE for newer Windows versions.
Is there a reason why there has been so little movement?
Do I think right that to avoid problems with TLS 1.0 you have to forbid it? This can take time.
I'll misuse my questions to answer Thomas Pornin because this doesn't fit into comment.
As usual, you write many letters :)
"RC4 breakage is still "academic"
Do you remember WEP history? 2001 only certain key patterns were vulnerable which could be excluded without changing the protocol, 2004 it was no more the case and 2007 only 40k packets were enough. Attacks never get worse, only better. And in real life, all updates need time, years will past till all servers update, although it's not so much like on soho routers. Can you predict with reliable probability when it will become realistic? About workarounds - are they backwards compatible? How long will they hold? Isn't it easier to use newer TLS version?
Upgrading client support to TLS 1.2 will not change anything at all until most servers are upgraded, too.
So upgrades need time, earlier we'll begin, earlier it's done.
comparison with IPv6
Well, with IPv4 you can predict when you are out of IPs. This depends much of the country - those who were first in internets usually have no problems :) Those who are out of IPs advance IPv6, like China.
In practice, several widely used browser rely on the SSL/TLS code of the underlying OS
Which ones O_o? I thought only IE does this, who cares about it with no working AdBlock.