Password hashing is concerned with brute-force attacks that take place offline using a dump of hashed passwords, not online against a running service. See this answer for how password hashes are usually obtained.
A running service does pay a cost when verifying passwords since it is not completely cheap. A strongly recommended step to take is to rate-limit the number of login attempts that can be performed, thus preventing the attacker from sending more than “a few” password guesses.
If there is no rate-limiting, the likely result would be the server CPU being fully consumed with password verification, slowing things down even more potentially to the point of crashing. This would be equivalent to a denial-of-service but would not result in a successful brute-force attack.
If the servers can handle it, it would still take entirely too long to brute-force due to time needed to verify each password (as well as the round-trip to the server).
Finally, there are password hashing techniques where the load is mostly on the client (eg: SCRAM), but this is more useful with heavier custom clients (eg: DB clients).