Yeah, cables can snap. Things go wrong sometimes.lol
But most of us that have failures like that are tuning are bikes for FAR higher top speed. Or the cables are old and worn. You really sound like you would appreciate a stock bike.
I'd look for a Puch maxi(sold as bombardier in Canada, but they went over the border all the time), an Italian bike with a minerelli engine(they were sold under many brands. The engine is the important part) or a sachs( also sold as Hercules). All of these are exceedingly reliable, but the first two are much more tunable. A Sachs will run reliably forever almost but tuning them is a chore if you want to go fast...reliability goes right out the window.lol
TONS of company's made mopeds, but very few made the engines really. The engine is the biggest part when choosing a bike, followed by build quality and comfort.