The trouble is we can only get "real data" by testing more people. If we test more people we will almost certainly discover the numbers are worse than they appear now.
All that is to say that the situation can only be worse than we already know. I'm not sure more data would lead us to isolate less at all.
You might be right that there could be large numbers of people with the virus who are doing just fine right now, but we know from nearly 200,000 cases (that's plenty) that a non-trivial portion of cases require hospitalization. That's the whole problem, right there.
So we know hospitals can be overwhelmed and a LOT of people die for it. Healthcare workers included.
We know the situation is probably worse than it looks, but we won't know how much worse for weeks yet.
So without real data, it seems to err on the side of caution is absolutely essential. This can bring countries to their knees within weeks, and it has.
What would you propose we do without real data?