> Eventually, in order for the private investors to make money, they either need to get profitable or go public.

Most (but not all, obviously) unicorns could easily be profitable if they chose to be. It would come at the expense of growth and R&D, but they would be profitable nonetheless. Growth is just valued much more heavily in the current market.

If you look at S-1s or even recent public unicorn earning statements, most of their losses stem from outsized increases in R&D/etc. expenditures despite healthily increasing revenues. The most recent example I can think of off the top of my head is Dropbox.