I wouldn't call it competing, but more in the line of stretching resources. Yes I agree that design changes would be difficult, but not impossible.
The core can't launch without boosters, it can't re-light its RS-25s and land on them. Salvaging and rebuilding the boosters was never particularly close to "reuse", and the new ones burn longer and reenter faster and further downrange, making things worse. The core needs higher thrust to get rid of the boosters, it needs to perform multiple burns in flight, and it needs to be able to reduce thrust by nearly an order of magnitude and still throttle rapidly and precisely over a wide range for landing.
This would be very difficult to achieve with hydrogen propellant, can't be done with the RS-25, and would realistically best be approached by clustering 7 or more engines using a hydrocarbon fuel...like Falcon 9, New Glenn, and Starship do. Changing the propellant to something denser drastically changes the dimensions of the tanks. The core will need its own avionics making it capable of independent flgiht and landing. It'd also have to stage much sooner to reduce reentry stresses, with the second stage providing much more of the launch delta-v.
Practically every detail of the design of SLS works against reuse. The changes to make it even partially reusable would constitute a complete redesign, discarding most of the Shuttle-derived technologies. At most you'd reuse some of the tank design, but even that would need major changes to insulation, etc.