Okay, so there’s still only nine billion more proteins to go before that breadth of samples is met in the experiment you propose. So we’re going to need another twenty million milliters of cells.
You keep confusing 1 new cell with 1 new protein. And… all the rest I wrote, all over again, about sampling depth.
The experiment you propose doesn’t actually constitute a test of the claim that the average density some particular function in protein sequence space is found at a rate of 1 in 10^10. It is nowhere near it in magnitude. You’re going to need more time. More time isn’t “unnatural”, it’s unpractical.