Kelly betting is a rare case where the difference between subjective and objective betting is actually a big deal, because any difference in those probabilities can make a large difference in the amount of money the Kelly formula says you should bet. I don't know the exact source, but there was a YouTube video on Kelly showing the impact of miscalibrated probabilities using simulations.

Yeah, that's why I mentioned creating a very generous distribution for the probability if you don't want the risk of being wrong. You can set up the maximization step just the same, and the wider the distribution, the more conservative it will tell you to be, until ultimately it says not to take the bet at all, since you have no edge. If you're really risk-adverse, you can go with a full min-max approach, where you bet as if the actual probability is unfavorable as possible. You just end up making suboptimal choices compared to someone who (accurately) puts a narrower distribution on the probability.

Also, your estimate of the true probability doesn't have to be that exact, if your edge is big enough to begin with. Once I made great profits (betting with fake internet points) just by naively taking the sample proportion from a small sample. In fact, the event turned out to be more 'streaky' than a weighted coin flip, but it didn't matter, since everyone else there was betting on vibes.

In any case, it's not like there's just the trivial Kelly formula, and woe to you if its toy model doesn't apply precisely to your situation. It's a general principle that can be adapted to all sorts of scenarios.