Old PC monitors (CGA and EGA) used ~3-5V signals, too. The reason is that, back in the old days, the video signals were generated by simply outputting a TTL logic signal (for 8 colors) or making a crude DAC out of TTL gates and a few resistors to get extra colors.
Back when resolutions were low, this worked fine, but as resolutions got higher and people wanted more colors, it got tough to build a high end (high speed, accurate) DAC that could drive that kind of signal level into properly terminated coax cable, so the PC world went to the same 0.7Vpp (1V with embedded sync, which is common in broadcast, but somewhat rare with computer video) standard used by television. The TV people had always needed lots of colors at somewhat higher resolution, and they needed longer transmission distances, too, which had driven them to coax cable a long time ago.
Arcades have not typically used very high resolution, and they never need to run the signal very far, so they've until recently avoided the use of coax and proper termination. Most VGA (480p) and higher arcade monitors do have 75ohm coax inputs, often on the familiar HD15 connector used by PC VGA and even earlier by the broadcast people, and accept 0.7Vpp signals on that connector, but the older monitors still just take "TTL level" video of ~3-5Vpp.
In other words, as usual, "it's historic".
Now, I don't have any explanation for the handbag thing.