Actually, it the opposite. here’s the home team win rates in north american professional sports:
MLS: 69%
NBA: 63%
NHL: 59%
NFL: 58%
MLB: 54%
However, teams hosting the SB in their own stadiums are 2-0.
https://www.chicagobooth.edu/review/home-field-advantage-facts-and-fiction#:~:text=In basketball%2C NBA teams win,American football%2C it's 57.6%.