Ask HN: What is the best time to introduce eventual consistency into a system?

Let us say, there is a relational db intensive SaaS application that is being tested for its capabilities. As more and more data is saved by customers, the operations become slower and slower, because the use case needs to go back to some of the data stored earlier(need to select, sort on some fields) and update some values. So the longer the customer has used the product, the slower the application becomes.

Is this the right time to introduce eventual consistency to the application so the newer saves can be done faster so the user experience is better? All operations are done on a single db txn, because we need ACID properties of the relational database. So in case something fails, rectifying it outside the context of the user request is going to be difficult for user.

This is the classic case of users outgrowing the capabilities of the application. Could anyone speak from experience or provide pointers to examples of what worked for others?