I am surprised that this happens in your area, it certainly doesn’t in mine (Wales, Hereford and Shropshire) for non-treasure items and for two fairly straightforward reasons; firstly, valuation (and it’s costs) is not a funded part of the FLO’s remit, and indeed could open him/her up to challenge -and secondly, for a non treasure item a museum ( or other State entity) has no right of acquisition and therefore advance valuations would be a pointless expense. Of course, should a finder wish to sell a non treasure find, then normally both parties will seek valuations informal or otherwise and hopefully reach an amicable settlement. I have recently undertaken to donate a Saxon coin that I purchased at auction (Noonans) as it is an important Herefordshire find to the Museum involving a £5k gift on my part , the purchase price was taken as the market value. That coin had been through the PAS and recorded by the EMC in 2022 without valuation - difficult anyway as a unique coin.
Even for Treasure items, valuation comes late in the formal process and then only after a wish to acquire has been expressed. If Treasure is disclaimed and returned jointly to finder/ landowner, it is up to them to sort out their financial commitments to each other - hence the need for prior agreements.
As I stated earlier, it does not appear that this coin, if indeed a find, ever entered the PAS process.
Jerry