So you want the exact same lockdown as we have now, just more enforcement?
The problem is, how to enforce? The police can't attend every house they get a report about saying someone has just visited. You can't realistically spot check cars as you suggested, you might catch the odd person 100 miles aways from home, but if I were ever stopped I would say I was on my way shopping, and the local supermarket didn't have any bread left if away from home, or I'm going to see my friend to get them some supplies. Impossible to prove otherwise.
I've broke the rules, numerous times, driving for exercise, usually a walk down the beach or through the park, just as you have, not sure what your point is. The rule was you couldn't drive for exercise, the police guidance that was leaked a few weeks ago wasn't a change in the rules, it was them saying what they could reasonably justify a charge/fine for. The fact is, you're complaining about people breaking the rules, while you are doing the same thing. I don't have a problem with you doing it, I think it's reasonable, especially if you live on an estate, people want to drive somewhere nicer, but you can't then have a go at others doing the same thing.