MAME = Multiple Arcade Machine Emulator.
The key letter here is the E = Emulator.
The BIN files are dumps of the original games.
SO if the original game wrote back high scores then the emulated version does the same (at least in the newer Mame binaries).
Games like Galaga, PacMan, Frogger do not save high scores in their original versions. You power them off - you lose high scores.
You exit the MAME game you lose the score Ie Play Galaga, leave Galaga, go to Ms. PacMan, go back to Galaga - no highscores.....etc you don't even have to leave MAME or reboot the PC.
There is an episode of Seinfeld where a Pizza shop is shutting down. George discovers that he still has the high score of Frogger. His one and only accomplishment from his youth.
He buys the machine, hires a pair of illegal Eastern European electricians - friends of Kramer - to hot cut the machine over to a mobile power source so he would not lose the high score.
He then proceeds to wheel the machine out the door and across a busy street in Manhattan. The overhead view then turns into a real life game of Frogger where he jerks the machine back and forth and left to right in order to safely wheel it to his home. Sadly the machine is taken out by a Semi-Trailer but George was able to jump out of the way.
You can find this episode on YouTube by simply querying Seinfeld and Frogger.
Getting back to your issue - for all things mame this is a better forum to join. I know there are some hacked binaries that do save highscores, but more often than not they send you to other games that are like PacMan or like Galaga
https://www.mameworld.info/ubbthreads/ubbthreads.phpI gave up on Mame about 4 years ago. I first started using a Rasberry PiII (linux based) to get away from Windows with the auto-updates, forced reboots after patching etc.
Finally I moved over to a JAMMA board. Basically, you use a harness, connected to your same switches, trackball, etc and 12v power supply. Power on the cabinet, and you boot into a nice clean interface - No PC booting, no windows updates etc. With the 14 in one boards you can select a single game so it always boots into Galaga if you want a dedicated cabinet, or you can leave on 5 of your favorites.
I recently upgraded to a 750 in 1 board. Loads of crap games in there that I will never play but there were a few that I was after that were not there in earlier versions.
Here is an ebay link to it. Not sure if it works but if you go to Ebay and type Jamma board or Game Elf you will see it pretty quick.
https://www.ebay.com/itm/295930316366?_trkparms=amclksrc%3DITM%26aid%3D1110018%26algo%3DHOMESPLICE.COMPLISTINGS%26ao%3D1%26asc%3D20231016072133%26meid%3D34710d0f2e2b41e2aed79b5b4da84867%26pid%3D101878%26rk%3D11%26rkt%3D14%26sd%3D355270810293%26itm%3D295930316366%26pmt%3D1%26noa%3D0%26pg%3D4406038%26algv%3DPromotedCompV5WithHighAdFeeWithKnnRecallV1PostRankerMode1PBoosterV3a%26fpg%3D2&_trksid=p4406038.c101878.m1851&amdata=cksum%3A29593031636634710d0f2e2b41e2aed79b5b4da84867%7Cenc%3AAQAIAAABIMQ4i4G0TKqdnw2r2UzGDkyandjT6VvGA4c5a09a1jXB%252FtL5ZfSL0e45uSSalrSlRcUgM%252FBdAChBvbEzUqW0PnjRJFMwvvI1E8LrL1hVNwomb0c8EaX6t0k6xww62oMNVQ%252Fm65FrNFx%252FOPQa65XShyseTtdwPa9AdcF1xxdN5bBfRPKiqyyOC6P37QdyJe2Gq8%252F1nhU7RQ89m2QxPE0Z6Dlkq43N8pw9c9CJ7fHKvWx1wKkWJwWAmlLU3QYTta6%252B8m7ir%252BA41ufW9vilkFIuO4QKy25UGevOir7jZ0NN04ftepo0gT830XCKJGAJTE7%252BO%252B7KT38wuTTxXnsxAWb4DFKnYU5uD3We%252Bmc7hnNpP1WqGWaLdp8lOUGgsiUn98eXYw%253D%253D%7Campid%3APL_CLK%7Cclp%3A4406038