The three-shaft design separates the fan from the LOW pressure compressor, not the HP. The LP is then often known as the IP (Intermediate Pressure).
Similarly, the geared fan arrangement allows a speed ratio between the fan and the LP(IP) compressor.
Semantics. I was thinking about it in terms of wanting to allow the fan and the HP compressor to both spin at closer to their optimal speeds (which for the fan would be slower, the HP compressor faster). Plus not all twin spool engines have a compressor on the LP spool. Plus on a 3 spool, the slowest spool, the one that the fan is on, still gets called the "LP spool".