(I think) my question is simple. I'm appealing to the experience of others to ask
Would you recommend carrying a sleeping bag while hostelling around Europe in summer?
I backpacked in Europe during summer and during my journey I was not willing to expend too much with hostels. Sometimes I arrived into cities without having a booking and could not find beds in cheap hostels. Since I didn't want to go for the hostels that were more expensive, after some talking, some of the cheap hostels allowed me to sleep in the floor using my sleeping bag for half of the price.
I also met some travelers that used the sleeping bag to sleep in train stations. In fact, I also did it once but just because I wanted to have the experience(I could have got a cheap bed in a hostel if I wanted to, there was no need to sleep in the station).
So, If you are willing to travel without making booking in advance and also don't want to expend to much money, you should definitely take a sleeping bag with you. Otherwise I recommend you to take it only if you want to use it as a sheet in the hostels since most of them don't provide one.
You can carry a sleeping bag for many other reasons but if you're always staying in Hostels my advise is no, don't bother.
In my experience most hostels provide bed-linen. When they don't provide it they will usually rent it. Using a sleeping bag is normally not allowed in such a situation.
Curious enough I once stayed in a hostel in Copenhagen and they rented bed linen. They didn't allow sleeping bags but they did allow you to bring your own bed linen.
If you know where you are going you should ask, but for example, in Berlin in hostels it's not allowed to use your own sleeping bag, so taking it was simply a loss of space and unnecessary weight. So I'd expect that in the rest of Germany it would be similar.
But taking a sleeping bag liner would be a good idea. It's very light, takes little space, will get you more warm when the coverlet is too light, and would give you more comfort if you don't trust the bedding.