Solid boosters are more complex and so Saturn could not have launched on time if they tried them. So for Saturn with a (arbitrary) deadline not doing them was the right call. Don't confuse right call with best call though: we know on hindsight that Saturn launched on time, nobody knows what would have happened if they had used solid boosters.
The only real benefit of SRBs is cost. They're dirt cheap and provide a huge amount of bang for your buck. But complete reuse largely negates this benefit because reusing an expensive product is cheaper, in the longrun, than repeatedly disposing (or "reusing") a cheap product.
The cargo bay was sized for military spy satellites (imaging intelligence) such as the KH-11 series, which may have influenced the design of the Hubble Space Telescope. Everything else led on from that.
Without those military requirements, Shuttle would probably never have got funded.
I'm listening to "16 Sunsets", a podcast about Shuttle from the team that made the BBC World Service's "13 Minutes To The Moon" series. (At one point this was slated to be Season 3, but the BBC dropped out.) https://shows.acast.com/16-sunsets/episodes/the-dreamers covers some of the military interaction and funding issues.
It's also relevant that the Space Shuttle came as a tiny segment of what was originally envisioned as a far grander scheme (in large part by Werner von Braun) of complete space expansion and colonization. The Space Shuttle's origins are from the Space Transportation System [1], which was part of a goal to have humans on Mars by no later than 1983. Then Nixon decided to effectively cancel human space projects after we won the Space Race, and so progress in space stagnated for the next half century and we were left with vessels that had design and functionality that no longer had any real purpose.
[1] - https://en.wikipedia.org/wiki/Space_Transportation_System
(Having a wing, empennage and landing gear greatly increased the weight. The only thing that really needs to be returned from space are the astronauts.)