Thats unsafe. It will cause random, surprise, state divergences; along with attacker triggerable ones. Such a thing needs a consensus system to decide on what the requirements are. This is what we have mining for. Consider an attacker who floods the network concurrently with many different spends all the time. Miners have no idea that other people got different spends (and can even be prevented because the information is simply out of their lightcone). Even if they have some awareness, they have no idea what the majority of the network is accepting. We have mining precisely to resolve this ambiguity in the state of other people's systems.