I think it still could work, but it'd need a proper lockdown period.
Logically, if everyone was given warning to get in food (and given a grant to do that, and to cover 2 weeks off work for most people, apart from key workers), and everything shut down - including schools and colleges for 2 whole weeks, the only people moving about would be essential workers.
If they had enough tests to test all essential workers through that time, and make sure they weren't spreading it, then the virus couldn't go anywhere. It would just die out as people who had it got well (or, sadly died) without passing it on.
After 2 weeks, if it was really strict, then presumably the only people still ill would be in hospital. That would be few enough people to track and trace, and once the numbers are really low it should be easier. The countries which do have a really good grip on this have kept numbers extremely low, and then they can put all their resources into tackling any new breakout really fast - leaving most of the population completely safe to do anything apart from travel.
I know it wouldn't work in real life because not enough people would probably stick to the rules now, but if it was possible, it would be such a good thing to do, especially for people who've been in various degrees of lockdown for weeks and weeks.
Yes, it'd cost money for the government to fund, but once that lockdown is over, then with enough testing packs, we'd all be able to do normal things and see people (carefully), so not so many jobs would be lost, and then we won't have so many deaths or people getting really ill, before the vaccines are approved.