The physics problem regarding radiator arrays isn't unsolved, but it's not a problem that scales up gracefully. Small-scale radiators could get by via passive cooling, but large-scale radiators need active cooling, and now you need fluid, pipes, and pumps that all represent additional launch mass and points of failure (and the pumps are generating heat of their own, so now you need more radiators...).

I think it's not necessarily about being the cheapest option, but a more politically acceptable one. I don't think you're going to get people protesting a data center in space considering it won't be next to their house, won't use water, and won't lead to increased electricity rates. I could see companies paying a premium to keep the political heat associated with traditional data centers off their backs.

With well considered engineering it doesn't even need to be tap water. If you have a closed loop thermal conductor that interacts with the components themselves you can then use really trashy contaminated water that just needs to be clean enough not to actively erode the heat transfer mechanism. We have setups like this all the time that use condensed air via cooling towers or salt water immersed heat sinks to discharge energy - it's more expensive than tap water but it isn't technically complex. So if it ever becomes unpalatable (likely due to politics) to use tap water there are some readily available alternatives.

The big win of being in space is just a worse alternative to using an intermediary heat transfer medium.