I’ll SWAG that nearly everyone who does such a switch does so for accuracy and/or speed at catching Hypos, not Sensor pain. BUT, I do remember, even 3 years later, that inserting the MM Sensor was vastly more painful than inserting Dexcom’s. (And the current Dexcom Sensor is even thinner.)
For me, inserting the Dexcom is less painful than inserting my infusion sets. (I use AccuCheck Ultraflex, a nylon infusion set-- so it’s wider than the steel ones going in, but less painful during wear.) While wearing the Dexcom, I don’t even know it’s there-- I often have to look or feel before going to bed, in order to find which side I’m wearing it on! But during the actual wear, I wasn’t much bothered by Minimed either: it was only the insertion which had me sweating in fear, and each time finding:
YEEOWW! My fear was completely justified, every time.
But there's two things which might be very bad about insurance paying for your switch. First, both of your CGMS components are still in warranty (i.e., the Minilink and the "feature" on the pump). Insurance almost certainly won't pay for new components, so the startup kit is Out-Of-Pocket (as you already guessed). More serious, and you might not be aware of it, is the vastly higher cost of Dexcom Sensors.
The cash price of a Dexcom “7-day” Sensor is currently $60 each (i.e., $240 per box of four). But Dexcom charges more for Sensors when they’ll have to mess around with insurance claims, insurance fights, and/or insurance paperwork: $100 each (i.e., $399 per box of four).
Some insurance companies, including mine, are in-network with Dexcom. My own, Wellpoint, doing business as (‘D.B.A.’) Anthem Blue Cross of Nevada, pays only a capitated amount, near the cash price, and Dexcom “eats the rest” as part of the deal. At $60, before Dexcom changed the ‘with insurance’ price, you could have made the argument that $60 for a “7-day” Sensor is cheaper than $35 for a “3-day” Sensor… even though, for people who keep their bG’s pretty stable, Minimed’s Sensors actually last longer than the Dexcom ones do.
But you say that you’ve got ‘great insurance’, so it definitely ISN’T WellPoint. Start by asking them if they would cover the Sensors, if you found it to be quicker at catching lows for you., as so many others have reported in themselves. Ref John Walsh, the famous CDE. (If you want it, you probably need to focus on the possibly better effectiveness, or visible signs of reaction to the Minimed Sensors-- NOT merely enjoying less pain during use or insertion.)