No, you weren’t allowed to strike in the USSR (actually you even weren’t allowed to want something like that), but trade unions were useful for an average worker even without any strikes on the horizon.

It sounds quite strange but Soviet trade unions (or, the main trade union or trade union of all other trade unions — ВЦСПС) were in fact very large touristic organizations. Thousands of hotels and sanatoriums and kids’ summer camps were owned by them, and for many members of the trade unions all these facilities were absolutely free or much cheaper than they should be. Yes, there was a good chance for the average worker to go on vacation with all main expenses (tickets and hotels) covered. Not all the workers could do that for free every year but it was a real possibility, millions of people used these facilities every year.

Also, trade unions often owned libraries and (I don’t know an English equivalent for that) so-called culture houses (дома культуры). Culture houses were, in my opinion, very useful facilities, especially for small towns: there you could see movies, attend some concerts or bring your kids to their hobby classes (you didn’t have a real cinema or hobby center if your town is too small for that, so these all-in-one centers were much better than nothing).

I want to add that the verb ‘own’ is not very good here, because many of these facilities weren’t profitable, trade unions spent their money on them just to have them around.

Unfortunately, I don’t think this comment is answering your question fully. Soviet trade unions were very influential, and it’s not really fair to describe them only as providers of free vacations, but I think it was the one of the main reasons why people were joining them without any struggle (another reason is people were supposed to do just that, and you didn’t want to explain why didn’t you join like all your happy Soviet comrades), and I think it could be quite interesting.