A worldwide, prison-like lockdown for 4 weeks is by far the best way of tackling this outbreak.
Unfortunately, that's not possible in any sort of practical way. Going to prison is considered a punishment which is why everyone tries to avoid it.
Yes, the scenario you posted is possible (though unlikely, so please don't get too paranoid). It's why we all catch colds and flus every year. But even a lockdown will require people being allowed to leave their homes to go food shopping .
All we can do is try to come up with solutions that practise the art of the possible, whilst also trying to mitigate the inevitable economic collapse (eg. people losing jobs, homes and having no money) and the subsequent social pushback.
We also have to factor in that even if eradicate C19 in our small corner of the world, it could continue to exist in Asia, Africa or America and boomerang back after we try to lift the lockdown.
Basically, the virus is going to eventually defeat all our best efforts and infect 70-80% of the world. We just have to try and slow it down at tactical times (informed by behavioural science and economics) so the NHS doesn't breakdown.
4 weeks would do nothing. Outbreak came from one person in China. After 4 months we are at 200,000 infected worldwide. You keep people locked for 4 weeks, chances are there will still be families where after those 4 weeks there's someone infected left, and we are back to square one. That's unless you lock everyone down individually, without any contact with anybody... then 4 weeks would be fine, provided you don't allow anyone to even go to hospital meaning everyone who is in bad condition dies. Any anyone who has any other condition in the meantime is dead as well.
There's no way out of this that doesn't involve millions dying.