I agree, any connection between the Egyptian "foot" hieroglyph and the lower case "b" seems irrelevant, but it seems that the Phoenician letter bet looks kind of like the Egyptian "foot" too, so perhaps that's where the connection lies.
The Wikipedia article for "b" seems to list both the "foot" and the "house" hieroglyphs in the development on the sidebar... not that Wikipedia is always correct.
I think the professor in that video is quite well known and has written several books on Egyptology, so I doubt he would be completely off base on something so basic. In any event, you're absolutely right that there the house hieroglyphs is related. I was wrong to question that. But it seems that the "foot" hieroglyph maybe has some relation too. If you find anything more about this, I'd be curious to hear what it is.
The Wikipedia article for "b" seems to list both the "foot" and the "house" hieroglyphs in the development on the sidebar... not that Wikipedia is always correct.
I think the professor in that video is quite well known and has written several books on Egyptology, so I doubt he would be completely off base on something so basic. In any event, you're absolutely right that there the house hieroglyphs is related. I was wrong to question that. But it seems that the "foot" hieroglyph maybe has some relation too. If you find anything more about this, I'd be curious to hear what it is.