My experience (real world, for actually existing code) is that property tests often require a lot of fiddling with the data generation, in order to actually stress your system in interesting ways. If you just throw "totally random" data into your system, you won't be testing very interesting properties. Amazing assurances and payoff from doing it, of course! Just like... "just generate random arbitraries" works a lot less when you're working with 100 field structs and only 10 or so "matter" in senses you care about.
To my knowledge I have not seen a property testing toolkit that leverages code coverage in the way fuzzing does.