Most PAKE implementations actually make a security trade-off here - they protect the password transmitted over the wire, but you end up with a weaker password hash stored in the server's database.
Modern PAKE implementations, like SRP, don't store the plaintext password on the server side, but rather store a "verifier", which is essentially a hashed and salted version of the password. This way the server never sees the actual password, even at the registration phase.
The problem is with the hashing function though. For instance, all the SRP implementations I've seen use fast hash functions like SHA-1, SHA-256 or Blake2b by default. But contrary to folk wisdom (which is unfortunately often repeated here as well), hashing and salting a password is not enough. This is not 2003 anymore, and rainbow tables are not your main threat - your main threat is a cluster of fast GPUs demolishing your hashed passwords at rates that often just start at 1 GH/s.
The best practice nowadays is to use a function which is both computationally expensive and memory-hard such as scrypt or the newer Argon2 (and not PBKDF2!). You could very well do that with a PAKE, but now you run across a nasty UX trade-off: the computationally expensive function would have to be executed on the client side every time the client authenticates. There are WASM implementations of Argon2 out there, so this is probably not a big issue on a beefy PC, but you'll have to aim for the lowest common denominator here, and tune your function for a low-end smartphone.
tl;dr: In practice, with a carefully implemented PAKE, you'll give the attacker a 10-100 times faster hashrate than you would with a plain-text password authentication approach implemented with the same amount of care. In real practice, you'll probably use whatever defaults your library gives you and give often end up with a ridiculously weak hash.
Now, I said this is a trade-off. If you implement PAKE well, you will reduce the resiliency of your stored password hashes against brute force attacks, but this is what you get in return:
* Protection against password sniffing at TLS-terminating proxies
* Protection against hackers taking over your server and stealing user passwords as they login (Online password leak)
* Protection against MITM with a stolen CA key[1]
All of these things are still an issue with clear-text passwords even if you're using TLS. If any of these issues are a concern for you, this means you consider your users' passwords to be significantly more sensitive than the data that flows between your clients and servers, but that could be a valid threat model. In this case PAKE looks like a nice solution.
For everything else, I don't recommend PAKE. It is harder to implement correctly (with library defaults being insecure as I mentioned above), and this is more important than whatever theoretical strengths it has. Cryptographic systems are generally broken because of incorrect implementation rather than theoretical weaknesses in the algorithm.
[1] Not very common, but that did happen in the past: https://en.wikipedia.org/wiki/DigiNotar