If you don't see the relationship between parts count and ease of maintenance, then you've never taken one apart and put it back together. 4,000 more parts take a LONG time to install or remove, and there is a LOT more opportunity to drop one inside an engine. That requirs even MORE time to disassemble it and find the part if it goes inside the engine.
There is a strong relationship between number of MOVING parts and relaibility. More moving parts means more parts to fail, simple math of reliability engineering. Parts count matters in reliability and MTBF.
I do not have an estimate of the number of MOVING parts in an Allison versus a Merlin, but I KNOW from being inside both the Allison has fewer moving parts.
When properly assembled, tuned and operated, both engines give excellent service, with the Merlin requiring more maintenance. For instance, you have to torque the Merlin cylinder liners every 25 hours or so while the Allison cylinder liners must be torqued once when being assembled and are never touched until disassembly after that. The Merlin method of torqueing in the valve seats is just plain stupid and involves turning it in until the new seat shank snaps off. There is some minimum torque, but no defined torque. That they used a method that produces no defined torque value for the seat does NOT make the Merlin a bad engine, it means there no defined torque for the valve seats, that's all. In operation, it doesn't seem to make much difference, but most good engineers don't design that way.