I had a car with push button start and a CVT. After putting the first 50 miles on the car, the brake light switch died. Nissan, in their ultimate wisdom, used the brake light switch to tell the computer if you are pressing the brake when starting the car. Well, no brake light switch, no starting the engine. Had to get it towed back to the dealership to get fixed.
Modern Nissan is pretty hit-and-miss. Their CVT transmissions have a bad reputation too. I have a new Acura with push button start and a manual transmission and all the electronics work correctly with no issues.
I used to have a 92 Honda accord. The car was built on par with Toyota as far as reliability. With that said though, there was one time it wouldn't start. Push started it, it worked,, but when starting- the problem persisted. Went to a shop to diagnose it. Turns out manual cars normally use a clutch switch to tell if you have the clutch pressed to start the car. There is a little rubber standoff on it to dampen the clutch pedal coming back up and hitting it, making it last longer. The little rubber bit fell out and got lodged making the switch not disengage. It was a 10 cent part that cost me an hour of diagnostic time (the minimum). So yes, manual cars still have an equivalent problem to what you had.
Why all the CVT hate? I drove a Jeep Patriot that had a CVT for about 100,000 miles before any major things broke, and what broke on me was the engine, not the transmission. That thing has great gas milage, as long as you used the CVT properly. Also need to swap out the air filter, oil filter, spark plugs, and plug wires, cause the ones that Chrysler puts on are crap, but if you do that, and keep your tach as close to 1000-1500 rpm as possible, I was getting 35/50 mpg.
The thing is, good modern automatics should last more than 100,000 miles. Motors should definitely last more than 100,000 miles, but from what I see online a lot that seems to be about the use-by date for Stelantis motors. Nissan (Jatco) CVTs were notorious for failing at or a little before 100k, and Nissan was one of the first (maybe the first) to mass adopt the CVT into their vehicles. It's sad because Nissan had reached near engineering perfection on their VQ/VK motors and their traditional automatics prior to Renault getting involved in their business. Our 2011 Armada, the gas guzzling bitch that she is, runs like its new with 200k miles on the motor and tranny (both engineered in the late 90s).