Nope, no keys. Even things like Humvees and 5 ton trucks didn't have keys.
We had cable locks on all our vehicles. We put 5200-series GI locks through cable loops on the steering wheels to keep someone from driving them anywhere.
Believe it or not, early WW2 Jeeps had key starters in some cases, and many key key entry to the glove compartments. They also had keys to prevent the spare tires from being taken (those came in handy in North Africa where you had to put guards on
everything, otherwise it would get stolen). But they didn't last long for obvious reasons.
Civilians don't get how stupid "Joe" can really be. "Joe" is the embodiment on that guy in high school you wouldn't trust with your
pencil, who is now entrusted with the lives of the guys in his fire team. Joe will always walk up to formation without his ruck sack, helmet, or even his rifle.
I once saw some national guardsmen drive off in a Humvee in the town I live in (long after I resigned my commission) and they left a M249 machine gun sitting against a tree! I threw it in the back of my SUV, prayed that nobody with a badge saw me do that and think I was stealing it, then set out after them. I caught up with them well down the state highway, cut off the serial commander's vehicle (lead, trail, and commanding vehicles in a convoy are supposed to have flags on them to spot them) and handed the belt-fed light machine gun to a
very surprised Captain. "I think Joe left this behind at that last red light," I told him as we stood in the middle of the road. He just stood there in shock.
The SGT driving the Humvee came up, thanked me, took it and put in in the back of the Humvee without that Captain ever saying anything. I've often wondered what happened to the guy who left it behind once all the vehicles were back at the armory...