That's a good question. The assembly of the Space Station would have needed heavy-lift boosters, or smaller modules. Manned trips to the Space Station are already done routinely using conventional boosters (Russian).

Obviously, recovering large payloads from orbit could only have been done with the Shuttle, or a similar system. Same for on-orbit manned work on delivered payloads. I don't know about things like the Hubble repair. Some form of dual launch and rendezvous might have handled the equipment transfer and human repair crews separately. It would make an interesting study.

SpaceX's "Falcon Heavy" is intended to launch Shuttle-class payloads for about $1,000/lb. We'll see.

There are many concepts for upgrading conventional rockets to have reusable hardware, such as recoverable engine modules or even recoverable stages.