We have no way to do any major service to the ISS now without the shuttle and the ISS retrofit was the main reason for the deferral in the Shuttles retirement.
By comparison the Saturn V has a 140 ton mass to LEO, 7x what the Proton-K could carry, and more importantly could have carried modules double the diameter of what the shuttle could put into LEO.
The unique selling point of the shuttle was the ability to return payloads from orbit to the ground for servicing, but as it turns out that was much more expensive than having a cheaper launcher and just launching another module.
Let's not draw the wrong conclusions from history. The shuttle was a failed launch system by any reasonable criteria. History has shown that plain old boring boosters were the right choice. The Soviets/Russians have been able to launch things to the ISS after the US lost its wings.
The only reason we have "no way to do any major service to the ISS" is not because the shuttle was so great, but because it was a dead end. The US has had to play catch-up with the COTS program with SpaceX et al.
MIR wasn’t only 4 times smaller than the ISS in terms of tonnage but it’s design was the same as the Salyut and Skylab the ISS was the first thing we can say we actually constructed in orbit.
The only thing that could have been somewhat complicated without Shuttle capabilities was returning the Mir solar panels, for detailed analysis of their faster-than-expected degradation.
https://www.americaspace.com/2012/12/20/what-do-mirs-solar-a...
That payload is small enough that it could have been put on a reentry capsule if it wasn't for the Space Shuttle.
So to a first approximation the ISS could have been over 2000 tons if NASA had just stuck with and scaled up the Saturn V architecture, which history has shown was both more capable and cheaper.
So no, the Shuttle isn't what allowed us to construct the ISS. Except in the narrow sense that the better launch vehicle had been cancelled, so it was the only project left to do the job.
1. https://en.wikipedia.org/wiki/Assembly_of_the_International_...