There's probably plenty of maintenance to be done if it's old. Bearings get worn out or at least need to be cleaned and greased. Chains stretch and cassettes wear. Brakes fall out of adjustment and pads wear out. I don't know about you but I find riding a cared for and silent bike to be such a joy. I honestly can't fathom how people manage to ride squeaky rattly inefficient bikes everywhere.
I had a bearing problem 2 years back, but I changed to new wheel and haven't encountered any problems since. It has coaster brake and overall has very little moving parts. The pedal squeeks and is bent a little, there's some clicks and clanks, but it works.
Belt and shaft driven bicycles do exist. You just wouldn't want to ride one, the loss of efficiency over chain requires you to make up for it with your legs and that is not fun.
Enclosed chain bicycles are kind of a reasonable trade-off.