The car starts cold at the touch of the key. When put in gear, it tends to stall. Then turning the key does nothing. The starter does not turn or click or anything. But even if it does not stall when put in gear, it still will not restart. Sometimes, it suddenly quits just idling and won’t restart.
Wait a while, and it starts right up. With the right coaxing, you might be able to drive it, but it’s chancy and if it stalls, you are stuck, maybe in traffic. I suspect ignition switch, maybe the starter solenoid (although that would not explain the stalling when you put it in gear) or crankshaft position sensor, if that could prevent the starter from cranking after a start. Or a combination.
Automatic trans? There’s a switch that is along with the shift lever mechanism. It’s supposed to keep the starter solenoid from working unless it’s in Park (and maybe Neutral.) Check owners manual. You’re right, crankshaft position sensor is not involved in a will-not-turn over problem (that is, starter motor will not run.)
with no idea what type of car/truck/vehicle this is, I would suggest looking very closely at the battery cables. Are they tight? are they clean? are they corroded?
Suggest to focus on the fails to crank problem first. Ask your shop to measure the voltages at the two starter motor terminals with the key in “start”. Both should measure at least 10.5 volts. Report what’s measured here. Probe from the terminal to the starter case.