It's like the red weed in War of the Worlds... First JFH and now JHC (with CHF being the focus.)
Defence is in somewhat of a downward spiral of resource versus requirement and the discussions about who/what/when a Force should be cut to save money isn't going away any time soon.
So (SH Fairey) you may be right that it would cost a fair chunk of coin to move a simulator to Yeovilton but some might say that it would cost considerably less over the medium term to look at the requirement for 3 services flying helicopters in support of the land and maritime domain. (Maybe few enough years that the big savings would happen in years 1-4 where this government wants to demonstrate savings prior to the big 'give away' pre-election softener?)
Instead of "why should the Navy operate helicopters in the CHF?" should the question not be: "With each service operating so few helicopters now and even less as we reconfigure to Future Force 2020, why are the 3 services all operating helicopters in support of the land battle from the sea and on the land?"
You can save some money by having 3 services fly single types (so only the RAF would fly green Merlin for example) but you save significantly more money if only 2 services fly helicopters at all and as a result are able to remove the manning structure from that service completely.
Assuming neither the Army or RAF want to spend their lives on frigates and destroyers with Merlin Mk1/2 and/or Wildcat, I'll assume the RN is one of them (but do let me know if anyone believes that not to be the case.)
The potential (objective) money saving in rough order of magnitude with the greatest saving at the top:
1. RN/RM flies all helicopters (RAF SH and AAC disbanded with pro-rata manning structures taken as savings.)
2. RN/RM flies all medium green and all grey, AAC flies AH and CH47 (RAF SH disbanded with pro-rata manning structures reduction in total RAF.)
3. RN/RM flies all grey, RAF flies all green (disband AAC with pro-rata manning structures reduction - less saving than RAF SH disbanding due to manning ratios.)
4. Defence helicopter command with 3 services still flying each type of helicopter.
If Defence wants to save serious money, chipping away at the edges is ignoring the (herd) of elephants in the room that is manning and service structures.
There are 2 domains - land and sea - connected by the air environment. An objective assessment might be that as all green helicopters are in support of the land environment (on land or from the sea to the land) and so they might reasonably be flown by the 2 services who currently have their genesis in those domain and each operate helicopters in them.
Defence is in a hole of quite staggering proportions. We can pretend that having 3 services in aviation (fixed and rotary) is OK but actually, it's not. We're broke. We need to do something about it.
An objective view might be that many decades of CH47 experience and a dozen years of Merlin experience wouldn't be thrown away if the personnel did the reciprocal of what they did nearly 93 years ago and throw away their surplus Russian uniform materiel and put back on the RFC and RNAS uniforms they carefully packed in their cases. (AAC and RN/RM ones are a little more modern now than those itchy RFC and RNAS ones.)
Anything that keeps 3 services in helicopters (in whatever sensible combination) is an opportunity missed assuming we remain broke.