Yes, it's a known weakness. You have to rekey every X blocks.
Further, every solution is going to have other machinery solving specific concerns.
You don't call XTS something else because you've used scrypt or PBKDF2 as the PBKDF.
Work is work.
Propose a scheme whereby you use AES-CTR to encrypt a 100 megabyte disk of 512-byte sectors, whereby the scheme "rekeys" every "few sectors". Be specific.
"It's unreasonable to debate with an unreasonable person."
Bye.