1) they provided Forward Secrecy (if you are compromised tomorrow, today's connection is safe) relatively to very long-lived key material—certificates that lasted years
If all an attacker has is your certificate key, with PFS it has to mount a MitM to eavesdrop, which does not scale!
If you can take a small key from a machine in country X and use it to _passively_ decrypt all traffic to a website globally, it's Bad News.
I wrote about it some time ago. blog.filippo.io/we-need-to-tal…
1) it caps the Session Ticket Encryption Key lifetime to 7 days and
2) it allows a Diffie-Hellman exchange on resumption, bringing back Post-Compromise Security.
If all you have is the STEK, you again need to mount a noisy MitM. Yay!
Which brings us to the new schemes to use puncturable encryption (which don't get me wrong, is super cool!) to provide it.
The problem is that this does not provide any Post-Compromise Security: the attacker that stole the whole key yesterday is not going to forget any of it.