Theres a restaurant I go to which plays music that youd expect from a fallout game. The old folks like it cause nostalgia but a couple other folks on the younger end have said something along the lines of "I heard this in Fallout New Vegas" its great, also apparently Big Iron played once and a bunch of old bastards and younger guys sung along to it. I wish I was there for it.

IMO, there's two main factors at play. First, the speakers in most stores suck. They have to buy them at volume (quantity, not loudness), and install them everywhere. The primary reason they have them is for paging, so they can make announcements and request that people go places. Music just gives the speakers something to do while not doing announcements.

Due to the amount of speakers they buy, and their primary purpose being for announcements, they don't exactly buy high quality speakers. If the store has existed for a long time (maybe 10+ years), then it's likely they're analog, so the quality is also affected by the amps they're using, and the cables, etc.

As long as the system can still do paging/announcements without issue, the business really doesn't have any reason to spend money on upgrading it.

For the most part, most companies have connected these to some kind of satellite radio or music streaming system (like Spotify, but more business centric). It's just plugged into the ancient sound amps for the analog system, often by someone who isn't an audio expert, so levels are often all over the place, sometimes to loud and blown out, other times too quiet and details in the music are too quiet to be heard.

As long as the speakers still perform the announcements/paging that the company requires, they don't care if the music sounds bad.

There's a lot more to say on it for contributing factors, but the main drivers for it are not to play music. With the shift to digital and everything needing to update their music providing device, coupled with untrained people doing the connections for the new music solution to an ancient speaker system, it's unsurprising that it sounds like garbage.