If you depart from your home or if you have an important meeting the evening before, the risk could be worth taken.
But if you are on travel anyway and you can avoid the risk just by sleeping in another city, it’s not worth to take the risk from my point of view.
Personally I would sleep in FRA anyway, just for not having to get up that early in Venice. Getting up for a departure at 7am means getting up at 4am or earlier.
Booking the whole connection on one ticket would be fine for me as well. Enough flights to the US to get rebooked at, if things going wrong and with the airline taking care of it.