Interesting idea. What comes to mind first is that it would make PoW mining very sporadic. Essentially each PoW group would have to wait a lot until they can work again.
I'm not sure what this method does better than having the same PoW methods running in parallel though.
If there's only ever one algo that will be accepted for the next block that means the difficulty retarget is also tied to that algo and can essentially get stuck.
For example, let's say there's a massive ASIC pool which gets taken down due to DDoS or something. Then there comes a block that can only be solved with this ASIC friendly algo.
What will happen is the network will slow down because it has to wait for the next block to be solved with a difficulty that cannot be changed until the block is found - however long that might take.
But if you have multiple algos running in parallel, in the same example above the chain would still be moving without the ASIC algo which means the difficulty retarget could do its job and reduce the ASIC algo's difficulty without having to wait for an ASIC block being found so that small ASIC miners could keep the ASIC chain moving.
Of course, you'd need a limitation on how many consecutive blocks are accepted by the same algorithm (has to be a low number, like let's say 5). Some coins are already doing it afaik.
When the big ASIC pool wakes up to a low ASIC difficulty they can only flashmine 5 blocks before having to wait for another algo to find a block.
But they might not even find 5 blocks even with a very low difficulty since the difficulty retarget can be very very agressive since it can't get stuck. You can even set the difficulty to near infinite for an algo if it's solving blocks too fast and still be fine because it can be taken back down.
All this means that you can balance each block's block generation rate more precisely and you don't have to wait for any algo.