Yeah I have really been tossing this scenario around a lot lately. While the rent income would be nice... these days you need to factor in as you say possibly a management company fee, then the increased property taxes since it is no longer your primary residence but a rental. This in our case can be 10x as much property taxes per year compared to what we pay now. Which would basically kill 2 months rental income. Lastly the increased homeowner insurance because it goes up as landlord insurance vs primary homeowner insurance.
As you say could sell & invest. I have looked into the US Treasury Notes for a term of 2, 3, 5, 7, or 10 years. Safe & at the end of the day at current 4.25% rates the interest on home sale would not be much different than rental income after expenses + zero headache. Of course there is no guarantee for rates in the future but you can lock in 10 years worth on the notes