Texan Space Yokel Chiming In
The big problem that the Shuttle had in the 1970's was it's a system in search of a purpose, instead of having a purpose everyone in DC would support.
Lobbing sats into orbit you could do much cheaper with a Delta or Ariane, chucking people up into orbit was doable with other systems, where it shone was repairing satellites and ferrying crews to/from the ISS but it was the 90's and 00's 25 yrs+ after they drew up the plans for it.
The hope was that once the first-generation Shuttles proved their worth, next-generation Shuttles would be less costly to buy, operate and maintain, bringing the cost-per-mission down to competitive rates with disposable launch systems.
An article referenced earlier about the changes in NASA also discuss the problems NASA had with the paradigm they wanted to push for space travel.
America had gone from a nation that traveled by railroad up through WW 2 to one that traveled by car and jet aircraft in twenty years, because we built the Interstate Highway system and jet technology made air travel incredibly cheap compared to before WW2.
There was almost a blind faith that government subsidies, technical know-how and commercial enterprise would yield as impressive results in space travel once they got the kinks worked out as they did with the above transport systems from 1945-1965.
The problem was that politically there was a tremendous loss of will and a rather empty pocketbook after 1973, which nobody seemed willing to deal with until Ray Gun Ronnie decided SDI sounded like a great idea in the 1980's. Then all of a sudden, we had a reason to ferry people and satellites into orbit a lot more often and a more open pocketbook to make more Shuttles and fund the support network.
Then the Soviets inconveniently collapsed, and we found ourselves with all these resources needing a new assignment.
My point is that you have to butterfly away several key issues IOTL for a better Shuttle.
One, make NASA a national priority executing a long-range plan to explore and exploit near-earth resources for the benefit of mankind. IMNSHO, the military's input had a lot of distorting effects both on mission and perception.
Two, make NASA a bit like Japan's MITI in collaborating with American and friendly nations' companies to find and pursue opportunities in space. The more civilian involvement/feedback, the more pressure on the Pres and Congress to spur things along. The more competition America has in getting into space and exploiting it, the better for how quickly and effectively we do so.
Three, don't ask the Shuttle to do it all as the first-generation reusable spacecraft. Always think about the next-generation spacecraft to do specific aspects cheaper and better. Corporations would do that themselves, once they had interests making them money and wanted to cut bottlenecks and excessive overhead, but government bridging the gap would take a bit.
Fourth, William Proxmire and other NASA critics in the 70's would have to be convinced that the national and humanity's long-term interests would be better served by NASA than some pork-barrel project.
Solve those problems, and the Shuttle would be the least of your issues.
I'm not saying we'd be living in a jetpack future if we did with a Hilton space hotel and a Pan Am shuttle getting us there, asteroid and lunar mining with manned missions to Titan , Europa, and so forth, but we'd be a lot further on the way to making those happen.