If you introduce signing into mining, then you will have cases, where someone is powerful enough to produce blocks, but cannot, because signing is needed. Then, your consensus is no longer "the heaviest chain", but "the heaviest signed chain". That means, your computing power is no longer enough by itself (as today), because to make a block, you also need some kind of "permission to mine", because first you sign things (like in signet) and then you mine them. That kind of being "reliably unreliable" may be ok for testing, but not for the main network.