No matter what chain you use, you're almost certainly better trying to compress the data you want to store so it becomes cheaper.
I don't know about other chains but bitcoin only allows 20 bytes of optional universal data per transaction. Some encoding strategies like run length encoding or other methodologies can help maintain data in a way. Also storing text as an alphabet or alphanumeric characters can be stored in 5 bytes or 6 bytes respectively and can use sub versions of bytes to store even more.
But bitcoins blockchain isn't made for handling this and will just push fees up for everyone else...
I was not aware of the 20 byte limit. That would also be problematic for storing text that you wanted to keep private or secure, since encryption could inflate the text so you would probably have to use some combo of encryption and encoding to get the job done it sounds like.
I think the "bitcoin isnt made for this" begins to step into the ethical debate which isn't really my focus, but I also believe that as long as bitcoin allows for such a use case even though it wasn't intended for that...it does not matter very much. Ultimately, if it becomes a problem for the bitcoin ecosystem as a whole then it will force a solution to be created or bitcoin will fail. Relying on everyone to abide by some ethical standard isn't a great practice so instead of saying "bitcoin should not be used for this" I think the argument should be focused around "If or when bitcoin is used for this..how do we solve for x?". In a way, relying on everyone to stick to what bitcoin should be used for means you're trusting humans to do behave a certain way which goes entirely against the grain of what bitcoin is about at its fundamental core, which is taking away the need to trust humans to behave a certain way.