I don't know if the inscription technique will be the dominant way to keep records on Bitcoin. I think there are plenty of other more simple ways to do it. One idea would be to hash a file and put the hash in the op return of a transaction. Now you can prove the files fidelity from this reference point forward. The sender and receiver could also have some role in the validity of the information to have more confidence it wasn't fake or wildly inaccurate. The cost of transaction fees would also create an incentive to put information that was as valuable or more valuable than the fee of the transaction. So there's three elements at play, the hash of the file, the key holders of the the transaction and the fees of the transaction that could all be used together to help verify the integrity of trustworthiness of information.

I think a tithe-like practice might emerge where people wanting to record information will send a transaction the burns some Bitcoin to the Genesis address for example. They would be sacrificing purchasing power for the small benefit of everyone else in the network, they would be paying a fee too which they could also choose to be generous with, and record a ceremonious event like a birth, marriage, death, ect. This could also be a way to make informational donations to the network forming a library of sorts. It could be called the museum of satoshi.