Whether it gets bought quickly or slowly, the same number of bottles get sold in total and the same number of people do or don’t miss out. The only thing that really makes a difference in that sense is whether individual consumers are buying many cases of a particular wine. If that is a problem, then it would make more sense for TWS to limit numbers of a particular bottle per person (as they already do with some wines) than it would to hide the number of remaining stocks.
I’d also point out that it can be quite helpful to know the amount of stock left. There have been times when I’ve filled out an order with a few cheaper bottles I might not have otherwise bought in order to get an order in on something that I really wanted. If I had known that there was no likelihood of the bottles I wanted imminently selling out, I might have waited a bit longer (and bought less overall).