Assuming that the network is healthy which means there are many competing miners for a block. It would not make sense for a miner to keep mining an already published block because by the time it will be able to find that block the blockchain is already longer compared to his chain. Even if there are nodes that would accept it the network will always select the longest blockchain.
For example, if we assume that the said miner can find a block every 1 hour and blocks are being found every 2 minutes in the entire network. The worst scenario is when it just mined a block. This means it is impossible for him to grab the block from an hour ago because there are already 30 blocks ahead of it.
Therefore, the best case to steal a publish blocked would be that when the miner found a block an hour ago. There is a chance for that miner to keep mining for that block and be able to be accepted. However, its chances diminishes as the blockchain increases. In this case every 2 minutes. Probably at 2 blocks that miner would not be able to submit its block and accepted in the network.
This would cost a lot for that miner since it has only a very small window to publish an already submitted block. It would be profitable to just be a good miner and find the next block which has more probability of mining it rather than mining with an already published block.
In another case if the network is not healthy and that miner can mine blocks faster than the entire network it would be a different story. But this only happens when the network is at its infancy.