For as long as it is monetizable that will be so. The more people use on chain transactions, the less affordable using the chain for data will be. There is not a lot of information that absolutely needs to be timestamped and broadcasted that can't be done cheaper elsewhere. So we'll see.
People who think they can keep arbitrary data out of the chain are in for a world of disappointment.
Discussion
How about actually using bitcoin and spend it (thus pricing out inscriptions) instead of crying and "filtering" them?
Yes. I think that's exactly the market force we will see. I think the effort to enforce policy is futile, especially in the long run.