I brew on my back porch with a small overhang covering. I cool to 100-120 degF and then put a cover on when it finishes. Never had any evidence of a wild issue.
I think the idea that “wild yeast” are outside, and “inside” is a sterile environment is misunderstood. There are bacteria and yeast both inside and outside. Being outside does not necessarily expose you to anymore “bad bugs” than being inside does. Neither environment is clean or sterile - so, take the precautions you would take making any beer. I brew inside, in my basement and I put a lid on my boil kettle once I shut it down and start cooling it. If I was outside, I would do the same.
If you cool quickly and pitch a large actively fermenting starter then any wild yeast that your wort may be exposed to in that short amount of time should not have the opportunity to grow and flourish before your desired yeasts take over and prosper.