Why do many large turbofans have a gap (of turbine blades) between the LP turbine and HP turbine?
(Source) Cutaway for the GE9X.

The gap you see is not empty. Marked above is one of the nozzle guide vanes (they have removed most of them for illustration purposes). Those vanes are analogous to the compressor stator stages.*

Labels 91 and 99 below are those vanes—sadly the stators and vanes are almost always omitted from 'drawings', yet they are as important.

(Source) Turbine stages of the RR Trent 500.

The reason why the diameter difference is steeper in the GE compared to the RR, is because the RR Trent 500 is a 3-spool engine.

In short, the vanes in both engines when omitted from drawings, give the illusion of there being a gap (wasted space).



* Nozzle guide vanes have nothing to do with the propelling nozzle at the rear. In turbine lingo, nozzle means the stator stage for the turbine.

On the funny side, here's a thumbnail from RR's own YouTube channel, absolutely bonkers exhaust. Don't trust illustrations.