My creaky memory is that LRBs were originally planned for the Shuttle, but the cost of developing them would've been a lot higher than the cost of developing SRBs. However, the running costs of the LRBs would've been a lot lower than for the SRBs. Unfortunately for NASA, the time when they didn't have the money was when they were developing the beasts.
That's the argument for the SLS starting with Shuttle-derived SRBs, but they're hoped to be cheaper because we already have something similar to start from, and theoretically require little development to use.
Solids have often been claimed to be cheaper due to their simplicity, but they had to do a huge amount of work to ensure uniform mixing, high quality flawless castings, lots and lots of testing of the finished product, etc, never mind shipping and handling the segments and assembly into the vehicle without damaging them, and the additional expenses of working around giant fully-fueled solid rocket motors. Think of how much money we've poured into just trying to adapt Shuttle boosters for other rockets...
I suspect the justification was political from the start. The Shuttle spread pork all over the country. Even if solids were everything they were advertised as, making huge, massive, delicate, hazardous rocket components in Utah for frequent flights (the Shuttle was supposed to be the cheap, reliable workhorse to replace
all expendable launchers, with dozens of flights a year) from Florida just doesn't make sense.