What are the drawbacks?
The most notable drawback to continually nesting relay chains is the increased delay of things like finalization, cross-chain messages, and other things from the outer chains to the main Polkadot relay chain.
For example, imagine the block time of all chains is 6 seconds. If you have 3 nested relay chains, you would expect that any cross-chain message from a parachain on the 3rd layer to the main Polkadot relay chain would take 18 seconds or more, since each layer would need to produce a block to the lower layer with the message in it.
Luckily, parachains which are in active communication can position themselves close together to reduce this delay, but as mentioned, there would still be lag between block production on the outer edges of the network, and block finalization at the main Polkadot relay chain.
I believe it is not possible since I haven't seen any example of it or a chain that does this.
As Rob mentions, the current implementation of the parachains protocol does not have all the required logic to supported nested relay chains, which is why you don't see them.
But you should expect that in the future, this will be made possible.