I think there is no problem if 64-bit block ciphers are used in devices or protocols that process small amounts of data, such as embedded devices. Encrypting $ 2^{32} $ blocks of data on such a device is practically unlikely.
There are lots of embedded devices where encrypting $ 2^{32} $ blocks is very common. Think about Wi-Fi or Bluetooth chipsets. It's very common to underestimate the amount of data that will be sent over a connection, and WEP had a giant vulnerability because of that (its nonce was very small).
Also, $ 2^{32} $ blocks is not some magical limit where security suddenly gets much worse. The chance of collision increases as more blocks are encrypted.
In particular, I know that short message processing speed was judged to be important in the recent NIST LWC project (Ascon selected as the final algorithm).
You're assuming that a 64-bit block cipher is somehow more performant for small messages than the alternatives. Whether that is true is highly dependent on the system and the hardware.
If the key changes frequently in the protocol itself, I don't think there will be any problems. For example, changing the key every time we encrypt $ 2^{16} $ blocks of data.
This requires keeping extra state and it requires more key management that must be tested. It also may require an expensive rekey operation more frequently for security. If your concern is embedded devices, this may be impractical, since rekeying is not always possible (think EMV cards, which definitely can encrypt that much data).
I think it's okay to use 64-bit block ciphers in environments that value efficiency. Even if there is a fast 128-bit block cipher, a well-crafted 64-bit block cipher (PRINCE, PRIDE, Midori, etc.) is expected to be faster (AES with AES-NI support may be faster than 64-bit block ciphers).
That may be your opinion, but I tend to disagree. In many environments, including many embedded devices (e.g., Wi-Fi and Bluetooth chipsets, EMV cards, and transit cards), AES is used and is standard. Oftentimes, those devices have some sort of hardware instructions for it, so it's going to outperform virtually everything else.
Even if you don't have AES hardware instructions, you have alternatives to 64-bit block ciphers such as stream ciphers like ChaCha20 (or ChaCha12) or AEADs such as Ascon. Implementing Ascon also gets you a cryptographic hash and other goodies effectively for free, since they all use the same permutation. Unless you absolutely need a block cipher (and if you're using CBC or CTR, you probably don't), those can be fast, secure alternatives that can provide 128-bit or better security using a simpler design without the downsides of a 64-bit block cipher. Simpler designs (given equivalent security) are good because they reduce the risk of unintentional (and possibly security-sensitive) error.
I'm not saying that there are absolutely zero cases where a 64-bit block cipher is the right choice. I'm just saying that with reasonable forethought about the implementation and design of the system, there are very frequently better alternatives.