2 part question.
- What are some blockchain-based messaging apps? What are their benefits?
- Could an NFT based messaging app be built? If so what unique properties would it have?
Answering in late 2021:
Some apps mentioned above have plans to implement built-in NFT matketplace.
For example, iMe Messenger plans to support NFT avatars and neurobots by Jan 2022 on their roadmap.
Disclaimer: I'm not affiliated with any apps mentioned above.
You should DYOR to find what's best for you. Those products are in different stages of development, some only have a whitepaper, some have made the product but got very few users, and some already have large user base. Things may change as time passes.