It is about boundaries here - in more ways than one. Once they get used to the idea that they have the free use of both parts of their own drive plus access via next door's drive to prevent them from having to juggle their cars on their own property (and the public road), they could very easily become resentful if they see somebody later 'depriving' them of it - even if it's just somebody wanting to take back use of their own property. If you got another car, I wonder if they would just think 'well, it was good whilst it lasted' or if they would feel aggrieved. I bet it would be the latter if you got one additional car and wanted to park one car on each section of your drive and wouldn't put it past them to try to browbeat you into putting them both on the top part, to make using your property more convenient for them.
People who never bother asking for favours don't actually see them as favours, but as enitrely reasonable actions to start with and then subsequently as their own rights.
There was a thread last year (I think), where OP and her husband lived in the second of three houses (as you approached them from the road) and there was a shared access for the use of all three properties. OP's husband was in the habit of parking his car outside their house all day to 'tinker' with it and thus completely blocking house 3's access to their own drive. His perspective was that there was loads of parking space out on the road itself (which apparently he was unable to use); if she (from house 3) really felt the need to use her drive, she could ask him to move, but if she knew that she was going to be coming and going a few times in the day, surely she should just park out on the road to avoid inconveniencing him by keep asking him to stop blocking her access! OP said she heard the neighbour harumphing "So much for buying a house with a drive" as she carried her bags back and forth to the road.
OP's husband thought that the neighbour was being very unreasonable by coming home at 11am one day (she was a nurse working shifts) and wanting to use her own drive when he had expected her to be out at work all day. He sounded like quite an aggressive piece of work, so the neighbour had taken to parking on the road instead of using her drive (presumably feeling bullied) and, because she had yielded by doing this, he then considered her in the wrong for wanting to stop the 'arrangement' which, to his mind, had been working well for everybody (well, for him anyway).
Are the neighbours generally at home for most of the day, OP (lockdown notwithstanding)? There do seem to be some people who think that, because a neighbour might be out for most of the day, they somehow forfeit the right to free access to/exclusive use of their own property 'because I'm at home all day and I need it, but it doesn't matter to you' and expect them to simply 'fit in' with what suits them. These are often the same kind of people who assume that, as homeowners, the street belongs to them, and if the neighbours who are 'only' tenants put their wheelie bin out half an hour early or have one single noisy party on a Saturday afternoon, they're taking outrageous liberties and it's straight on the phone to their landlord to 'report' them.