I am a bit confused about Sponge construction and Merkle-Damgard-style ones for hashing. The only advantage I see for sponge construction is that they are secure against length extension attacks. So if the application does not mind about such an attack, Merkle-Damgard should be better, Is that the case? My intuition is that to hash long messages with sponge ones every block message has to be smaller (due to the rate of the absorption) while in Merkle-Damgard they can be longer and so hashing is faster.
Let's consider the cipher/permutation MiMC where the length of its input is set to $n$. One can use the permutation form of MiMC in the sponge structure. Thus each call to the permutation absorbs a message-block of size $r<n$ where $r$ is the rate of the absorption in the sponge. If we use the cipher form of MiMC in the Merkle-Damgard structure then each call to the block-cipher absorbers a message-block of $n$ (e.g., by Miyaguchi–Preneel for generating the compression function). This means hashing of the long messages is faster with Merkle-Damgard (when the same cipher/permutation is used in MD/Sponge).
Putting together, if the length extension attack is not a concern (like in the integrity of computations, SNARK), then the Merkle-Damgard construction seems a better choice (where the cipher and permutation used in MD and Sponge are the same/counterpart like the above example for MiMC). Is the above observation valid?
note: For MiMC the permutation is the same as cipher where the key is set to all zero bits (https://eprint.iacr.org/2016/492.pdf)