In theory the 3-spool design allows tighter optimization of all 3 for their respective role in what becomes a 6-stage bucket brigade with a fire in the middle. At the same time each interaction between the spools needs to have stall resistance built in. Avoiding those “impedance mismatches” I mentioned earlier is not easy or cost free. Something is also lost at each stage transition.
Whether net, net the extra complexity buys enough real world improvement to pay for itself seems unclear to me. Of the major manufacturers, only RR has developed and persisted for 30+ years with their 3-spool design. Nobody else sees the same need on even their experimental future tech engines.
Although as @Dr.Strangelove just said, is that difference a sign of organizational flaws? Either Not Invented Here syndrome for everyone other than RR or conversely for RR “this is the only secret sauce we have so of course we ride it as hard as we can as long as we can; even well past its sell-by date?” Hellifino.