It doesn't have anything to do with specificity, the Space Shuttle was just the only manned spacecraft powerful enough to get out to Hubble's orbit and back, and that had an airlock so you could actually access Hubble.
The Space Shuttle is the only vehicle ever built that can do in-orbit service. It's not that the Hubble is special in that regard, it is that the Shuttle was special.
ISS has airlocks that allow you to leave without removing all the air from the rest of the ship. Vehicles like a Dragon can attach their port to ISS, board, and then perform a space walk through the ISS's airlock.
Hubble is different. It's not like it's a ship that you can board. So you need two things: Ability to attach yourself to Hubble, and ability to leave Dragon to perform a spacewalk. It's not clear whether you can just have everyone in the Dragon suit up and open the hatch. And even then, you still need to attach yourself to Hubble somehow. I think you can via the port... but then you can't leave. Unless you go out the other door? Can you open that from the inside and get out with a space suit?
My rambling isn't meant to be an actual answer. It's more to show that it's wayyyy harder than "Let's just send up some people to Hubble!".
These problems could be solved. However no current space craft is designed the right way. Maybe it is a trivial modification to Dragon (making it bigger...), maybe it is better to start from scratch. That is a question for domain experts who probably haven't given the idea enough consideration to give a good answer.
> So does this also mean that the ISS is no longer able to get serviced, or are there projects to work on in-orbit service vehicles?
AIUI, The ISS can be serviced from the ISS if the appropriate supplies and personnel are sent up, but it doesn't have the delta-V to zip around other orbits servicing other satellites, so it is okay without the the shuttle for itself, but doesn't substitute for it for other things needing orbital service.
All the operating human launch systems are just capsules meant to either free fly or dock at a station, they don't have airlocks to let people out so using them for a Hubble repair would require a lot of modification and danger to use the whole capsule as an airlock. [0]
[0] Except Soyuz I guess their orbital module would allow you to keep the descent module pressurized but it's still way outside the design so there's no telling if the module would remain operational.
Soyuz has been used for spacewalks before, and the cabin is tolerant of vacuum. They haven't done that in ages, so it's possible that's been optimized out, but I'd suspect that requirement's been respected over the years.
Neat, didn't know that. There are of course other issues like how do you keep them in proximity while you do the work that could stretch days, ships don't usually free fly that close to each other for long the Hubble missions done with the shuttle all included hard captures of Hubble with the Shuttles.