Mugen is not expensive. I once bought a 1400 Mah replacement battery for mre previous smartphone (HP Pre 3) for a dirt cheap price at their web store. When I now boot up my Pre 3 (it's been a while, but sometimes just for fun and nostalgic) the battery is still at about 98% health. We're now at about 2,5 years since I bought that battery and close to 2 years of daily driver usage (the past months I've mostly been using my Jolla phone) so the quality is very good, esp. for that dirt cheap price.
(They also sold a well-priced 3000 MAh version but I didn't want to make the phone any bulkier lol.)

So no, it might not be more expensive for the Jolla phone (esp. because their sales of Jolla replacement batteries will be just as much as for the Pre 3).