I used to like going to pop concerts when I was a teenager.

[Nonverbis]

Advanced Grammar in Use by Martin Hewings



The answer key gives only 'used to' as the correct anwser.

Could you clarify why? Because it is a state? Or because 'would like' is a set phrase for a polite request?

 

[tedmc]

Only the past tense, "used to like", works when talking about things in the past. "Would like" is not in the past tense.

 

[5jj]

Could you clarify why? Because it is a state?

Yes.

Both would and used to can be used for repeated past actions, but only used to is used for past states.