However, the fact that only goats were revealed is also strong evidence that the host deliberately avoided opening the door with the prize, and therefor switching is a winning strategy.

This is an important point for, say, thinking about what to do if a quantum random bit turned the same 1000 trials in a row. The theory doesn't promise "chaotic" random sequences, a sequence that repeats the same outcome is as normal as any other. On the other hand, the repetition sequence could happen for some other reason, and it's this alternative possible reason that makes the sequence special, not the default hypothesis where the "strange" sequence is ordinary.