It will be slower to encrypt and decrypt, and a bit more complicated due to the multiple layers and managing the keys to encrypt and decrypt it all.
There's no disadvantage in terms of algorithmic secrecy.
There's no disadvantage in terms of algorithmic secrecy.
While I can't offer you a formal cryptanalysis, I do have a handwave-y thought experiment & proof by contradiction for intuition:
Consider two encryption algorithms A[...] and B[...] that are "good" in the standard ways (adversary cannot decrypt messages without keys, keys cannot be leaked by chosen plaintext attack, etc).
If putting A inside of B like B[A[...]] renders the system insecure, it would imply that B[...] was not a "good" encryption function! (if it was good, it would not break just because the input message happens to be the output of A[...]).
Therefore by handwave-y proof by contradiction, if A[...] and B[...] are "good", then A[B[...]] should be OK.
(Disclaimer: Again, this is a casual thought experiment and not real cryptanalysis. This result may not be true under formal cryptanalysis.)