As far as I know the only disadvantage that XEX has when compared to CTR is that you need a block cipher/permutation while CTR is fine with just a hash function. Meanwhile XEX offers the advantage that it is more misuse-resistant (reuse of the counter/nonce breaks CTR but this is not an issue with XEX) and less malleabile. Considering that, why is XEX almost never used outside of disk encryption?
If CPA-security is sufficient, then CTR is sufficient. If you need authenticated encryption (or CCA), then neither XEX/XTS nor CTR is sufficient and you should be using AES-GCM or something similar. In general, as soon as you want something that is "less malleable" then you consider malleability a threat and you should be using authenticated encryption. If you are worried about nonce misuse resistance, then likewise you should be using such a scheme (SIV or GCM-SIV, etc.).
There is just no good reason to use XEX/XTS, except when you have a severe limitation like in disk encryption that you cannot increase the sector size.