The RR concept of having a triple spool layout on it's bigger engines also negated the need for more complex VSVs throughout the LP/IP compressor such as needed on PW JT9 and GE CF6.
Having said that, with the advent of the Very Large Engines such as the Trent, RR felt the need to add VSVs & VBVs to the design to get the required results.
The joke going around RR when P & W said they were going to build a geared fan engine was that it would be 'a two and a half spool engine'. (you had to be there I suppose

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As for a variable pitch fan.... I think the complexity of this would negate any efficiency gains. The closest anyone came I suppose was the Unducted fan contra rotating efforts of the 80s.
What ever happend to them? Last I heard was the Russians were fitting them to a big 4 eng transport.