The newly disclosed research clearly demonstrates that the common parameters enable "precompute just once, attack fast everywhere" whereas when everybody simply generates their own values that approach becomes impossible. The difference is between the days of computation versus the seconds in their example.

The difference is many orders of magnitude, it is if everybody everywhere can be attacked anytime or just somebody sometimes somewhere.

Moreover, the main reason why it should be done is that the expected browser updates won't block the sites with 1024 bits. So all the sites which for whatever reason still use 1024 bits won't be so vulnerable if they had their own parameters.

The practice of using the common parameters already now worsens the current state. The bad effects of the really bad move already exist. The common parameters are now provably bad and it won't change in the future. Just don't use the common parameters. Generate the new ones everywhere.

And, of course, "minimum 2048 bits, please."

Edit: audi alteram... means "listen to the other side." Which side is the other side here? The stale information is not "the other side" it's just stale.