I agree with you OP.
I think the idea that keeping car parks and public toilets shut will discourage people from travelling is misguided.Ideally of course people should not be going out for so long that they need to empty their bladder or bowels, but I think it is hopelessly optimistic to believe that everyone will abide by that. Once they have been given the ok to travel then lots of people are going to do so. Some will be excited to get out and won't even think about toilet facilities, some probably don't really believe that there is absolutely nowhere open, and sadly some just don't care. I live in a fairly touristy area, but outside the most popular part and even here I've noticed an increase in cars parked on verges and along narrow lanes. It might not be illegal, but it is definitely not sensible. Friends who live closer to the real tourist hot spot have told me that the congestion has been significant, bins are overflowing and visitors have been relieving themselves in bushes etc. Rubbish has apparently included dirty nappies and discarded PPE.
Now I know I am lucky to live in a beautiful place and I quite understand why people want to get out and get some fresh air, especially whilst we've had such lovely weather. If I lived in one of the nearby towns I would probably want to come for a walk here too. But if people are allowed to come, then we need to provide at least basic facilities for them. It has to be safer to have car parks open, even if only alternate bays, than to have cars parked inches away from each other on narrow lanes. It has to be safer to have public toilets open than to have piles of human waste on beaches and in parks. Toilets in essential work places and public buildings like hospitals are still being cleaned so why not public toilets? Obviously each block would have to be shut for the time needed to clean and the cleaners would need full PPE, but there must be a way. Or if it really, genuinely is too dangerous to have people cleaning then it is still to dangerous for people to be allowed unlimited travel time/distance.
It needs to be one thing or the other. Either we can travel where we like and basic facilities are provided, or we need to be restricted to a certain distance or travel time from home. The current half arsed arrangements are not working as far as I can see. Maybe most of us are responsible and sensible but there are still too many who aren't, and if self regulation doesn't work, the authorities need to step in.