Why didn’t Nasa cluster four solid fuel shuttle boosters around an Atlas V booster. The thrust would be substantially more than that of the SLS, with no fueling problem on the launch pad. It would be much less expensive and if using old technology anyway, why not develop new technology while building a base on the Moon which should have been done decades ago?
The difficulty is that rockets are not made of Lego, you can't just bolt on an extra couple of rocket motors and expect nothing to change. It would be a bit like trying to bolt on an extra set of wheels to a car.
SpaceX found it far more difficult than they had at first thought to create the Falcon Heavy from three Falcon 9's. The inner core section had to be considerably modified to allow for the greatly increased thrust and the same would be true for SLS. It would effectively be a different rocket although it might look similar.
Yet another “why don’t we just graft X to Y?” notion.
You don’t work in systems engineering… or validation/compliance, flight-like testing, safety/quality, project management (scheduling/budgeting), etc.
Changing one part of a complex, slim-margin, high-consequence AND high-dollar system results in: a new system, with new risks, failure modes, effects chains, and thus verification schedule… and thus verification cost.
“ It would be much less expensive ”
No, it wouldn’t.
“ why not develop new technology “
??? Why develop new technology??? Do you think the question is its own answer- circular logic?
“ while building a base on the moon which should have been done decades ago?”
For what- is this another ill-posed question, let alone a circular question? Are you not aware of chondrites versus differentiation?