Social distancing seems without alternative, but there is one thing I don't understand. Maybe it is a stupid question, but why don't we massively, massively exp

Social distancing seems without alternative, but there is one thing I don't understand. Maybe it is a stupid question, but why don't we massively, massively expand testing. Then put up checkpoints everywhere, and don't allow anybody to pass without a current test (say older than 36 hours). If you have any symptoms, you are restricted to your house (I have a cough right now, and I find it insane that I'm allowed to go shopping or to work - nobody can be sure that it's not Corona). And if there's a confirmed case in your area, there is a curfew and extra testing. Apart from that, there would not be many restrictions. I guess this might be difficult in some countries, but here in Europe this seems like the best option - and a variant was successfully implemented in South Korea and Singapore. Why don't we go this route? Is there just not enough testing infrastructure available, or is there another argument against it?