I’ve done it with hefeweizen a couple of times. Left the lid just sitting on the bucket, lifted it a few times a day to be quasi-open fermentation. No infection and beer came out great.
Yep - I do this most of the time for my primary fermentations. I either use a piece of foil loosely over my carboy, or lightly place the lid on top of the bucket with a dry airlock just to seal the grommet. No issues so far over typical ale fermentation times of a couple of weeks. I wouldn’t do this for a long secondary, but I’m lazy so it works for me for primary.
I have done this with no off flavors. You want to keep dust from falling into the fermenter. Bugs and critters are on the dust. Bugs and critters don’t have legs, so they don’t crawl in.