I have had this issue with only 2 phones (of probably 100), one I repaired and one I purchased knowing there was a home button issue.
The phone I repaired: put a second new screen in and the problem was resolved (which made me confident to buy the second phone)
The phone I purchased… Still having issues. I have connected and reconnected the HB and it will either be too sensitive or not sensitive enough.
There are most definitely several possible issues with these.