As everything it is a tradeoff, a lot of things do not deserve a proof, but for the ones that do you are a lot more productive.
It also depends on the level of the proof, I want to make sure the idea is valid and it takes some time to know what to abstract and what not to (it is a model after all). So if you are aware of what you are testing and at ehat level the tool and your proof is working it is very beneficial
Managers don't want that though, for reasons that already Dijkstra has outlined.
Proofs are hard and often not for interesting reasons; its stuff like proving that you won't overflow a 2^64 counter which you only increment (aka something which won't happen for another couple billion years).
Current tools are only useful for specific kinds of problems in specific domains; things where a life really depends on correctness. Outside of those cases, lightweight techniques provide much more bang for your buck imo.