No, I live in the US, where I've known of people who got arrested for DUI because they were sleeping behind the wheel of their car in their own driveways. Some aspects of our criminal justice system are gravely flawed and nonsensical. You can look at instances of people getting decades in prison for marijuana possession while a child rapist got sixty days to see that.
For every person you've known, I'm sure there's many others in the world who've slept safely in their cars. Therefore, believable.
Your snideness is not really furthering this discussion. My point--which you seem to be purposely ignoring--is that sleeping undisturbed in your car in CERTAIN PLACES may come off as difficult to believe. It's not a big issue at all, and it can be easily avoided by 1) not having the character fall asleep behind the wheel, and 2) not fall asleep in an area where they are likely to be found by police or security guards who will make an issue out of it. Another poster already suggested such a place, and I don't see you jumping down their throat about it.
Now here's a question: Did they get arrested for being asleep in their car, or did they get arrested because, upon being rousted out, they blew over the limit for blood alcohol? I suspect, the latter. I remember family vacations as a kid when my dad, to save money, would pull the station wagon over to the curb in some residential neighborhood, and we'd all go to sleep in the car. That was back in the 1960s, but no one ever bothered us. And now that I remember it, in January 1994 I was on my way back from North Wales when I was stopped and ticketed in Cheltenham, England, for misjudging and running a red light. My blood alcohol test came up clean (as it rightly should have), so the cops and I all concluded I was just overtired. They told me to be careful the remaining hour it would take me to get home to Oxford, but said next time, if I was feeling sleepy on the road, I should pull over and have a quick kip. As it turned out, my exhaust manifold was loose and my perception was off due to mild carbon monoxide poisoning. But the point is that in that county, at least, it was law enforcement who advocated taking a nap behind the wheel! Where it's not allowed, that could be a matter of local ordinance, and in those cases the offense might be "camping without a permit." So if @deadrats wants his MC to konk out in his properly-pulled-over vehicle, he can have him do it in a jurisdiction where that's ok. And if there's any fear here that readers will question that, he can, as they say, hang a lantern on it.
You can't be done for DUI if you don't have the keys in the ignition or on your person , it also helps if you aren't in the drivers seat (at least in the uk) on the many occasions I slept in my car after a night out when I was younger i used to put the keys in the glove box , and sleep on the back seat (or on the passenger side if in a two seater) On the occasions when i was disturbed by the cops they were usually happy that i'd taken the responsible decision not to drive while intoxicated and would leave after warning me that you can still be over the limit when you wake up.
If the climate is warm enough, he can sleep in his car. If I've been in a situation similar to that, I've just stayed at my friend's. Sleep on the couch or even on the floor. A 2-hour cab ride or commute home seems unwise 'cause he'd need to leave his car behind, so it'd be smarter to just sleep it off. As for the type of car he'd be driving. I've no idea what's the "car demographic" like in your area. I would've suggested something from between 2000 and 2010, but if it's typical to drive old cars over there, then go for a '90s model (Our VW is from 2009 and it's considered old already.). If you observe the makes and models around you, you probably get a pretty good idea of what's common and "average".
In actual fact, it's encouraged BY police in most places to stop (in a safe and permitted place) and take a nap in your car, if you are feeling overtired. This will not apply if you are drunk, however. You can be charged for being 'drunk and in charge of a vehicle' —I believe that's more or less the terminology—and that's against the law. If you've been drinking, probably don't get into your car at all. I suspect if you take the precautions @big soft moose mentioned, you MIGHT get away with it, if the cops do turn up—especially if there truly is no where else to go. But I think it's all down to their attitude, really. And the morning after is definitely a problem.
Depends on the officer and the state in the U.S. I've heard of (but not known) people who've gotten in trouble for not having their keys in the trunk of the car. If the keys are anywhere in the cab and you're drunk they can make a case against you, or so I'm told. That said, for the purposes of this story I think the MC can sleep in his car, be just fine, and it's all perfectly believable and responsible.