The probability of a block hash being all zeros is the same of all being ones, and the same of odd digits being ones and even digits being zeros, and the same of being every other number.
So the problem created by a future block having the same hash as the genesis block or the block the genesis block points to as its previous block is the same problem of any future block having the same hash as any existing block today. It would not be a special problem.
It's currently believed this have a very low probability to happen, as there are not known SHA256 weakness.
In the practice, however, if something so unlikely happens, maybe some software like wallets or block explorers use the 'zero' value to identify the genesis block and present some bug or erratic behavior. Maybe some miner even mines another block on top of it, and then it broadcasts the new block to the network, where it may be rejected as a sibling of the genesis block, being regarded as part of orphaned chain.