Bear in mind that the reason Engine manufacturers produce engines is to make money.
The development of the original, 3 spool RB211 sent Rolls Royce broke!
After government intervention, the bailed out company had the technology to build upon, and now produces the very efficient (if a little finicky- ala BA 38!!) Trent.
It is interesting that the US manufacturers have never gone down the triple spool route, but are leaping past it to the geared fan solution for optimizing low-to-high pressure gradient.