It is possible to repair it and we know that because it was repaired many times before. It’d need at least some brand new hardware though.
Until reusables make it cheap to launch a replacement (and so cheap the replacement doesn’t need to be built as carefully and expensively) it’s preferable to repair it. Or not, as ground-based observatories have evolved considerably since the Hubble was launched.
Possible covers a broad range of effort levels and outcome risks. At a minimum a solution for controlled deorbit is required within 10 years or so. You'd think that something that could use the SCM [0] to catch it could also reboost it or stage a human repair mission, but some involved are not as sanguine as a lay person.
"The last time we went to Hubble, it was on the space shuttle, and it was quite a long time ago," Clampin said. "And, of course, Hubble is an old spacecraft now; a lot of the people who were very involved in the early serving missions have retired and there's a lot of work we would have to do to get back up to speed on how to do that." [1]
On the other hand, even keeping a program running while a solution is developed might be too much given the rules NASA must follow. "Announced on Wednesday is the cancellation of the VIPER mission to the moon, this is shocking because the Rover is finished construction and just needs a test session. Moreover, NASA is contractually required to pay Astrobotic to fly a NASA payload to the moon, so they have to pay for this anyway. Instead of a rover NASA will send ballast to the moon." [2]
Until reusables make it cheap to launch a replacement (and so cheap the replacement doesn’t need to be built as carefully and expensively) it’s preferable to repair it. Or not, as ground-based observatories have evolved considerably since the Hubble was launched.