Unfortunately there is no such thing as "Generic BT receiver". There are many different BT chips, so it will bring a lot of problems to find a compatible BT receivers and drivers.
And besides the driver BT needs additional software support. It also requires a pairing procedure.
All this complexity is beyond the MiSTer philosophy of easy use.
I think we have enough alternatives to generic BT:
1) USB-RF gamepads with their own receivers. For example Logitech F710. I've bought it couple weeks ago so cannot say now about battery lasting, but i'm long time (2+ years) user of Logitech K400r RF combo-keyboard and for the whole period i've changed the battery only 2 times! And i even don't use power off switch on keyboard - so it's always ready to work. If F710 gamepad will work the same then it would be wonderful!
2) Specialized USB-BT receivers (8bitdo, Mayflash) for selected A brands gamepads (PS3/PS4/XB1/Wii) which basically covers the need of 99% users, cause the quality of these gamepads is high.
So, only Chinese BT gamepads are out of scope. Not a big loss comparing to the support BT hassle.
P.S.: about the Logitech K400r - this is the best keyboard for MiSTer! It's really nice featured compact RF keyboard with touchpad. And basically you may forget about batteries as they last "forever"
If you want this keyboard then hurry up! Logitech replaced it with newer model K400Plus which has reduced cursor up/down keys making it unsuitable for many tasks - especially if you like to play on keyboard. That's why i've bought recently second K400r and store it on shelf. That's in case if the first keyboard will break later