Unfortunately, the database's primary keys (not auto incrementing) are also managed by a custom ORM by querying a MySQL function that returns the next set of ID's to be used. The ORM then caches them and serves them up to the application. The database itself is an ever growing 2 TB's of data, which would make downtime significant.
I had planned on using Dapper as I've enjoyed ease/performance in the past, but weening this database off of this custom ORM seems daunting and prone to error.
My humble opinion:
A rule of thumb when you deal with legacy code is: if something works, keep it that way. If necessary, make a change or an improvement. The main reasons are:
Besides, it depends a lot on the plan of the company the reasons to change (adding a feature, fixing a bug, improving design or optimizing resource usage). My humble experience tells me that time and budget are very important, and although we always want to redesign (or in some cases, to code from scratch), the most important is the business objectives and the added value.
In your case, maybe it's not necessary to change all the ORM. If you say that the ID's are cached, a better approach would be to modify the PK's, adding on them the identity property (with the properly starting value on each table). After that you can delete that particular part of the code that get the next Id's.
In some cases, an unnormalized database has his reasons. I've seen cases in which the data is copied to the tables to avoid the join, which affects performance. I'm talking about millions of records...
Reasons to change the ORM: maybe if it's inefficient, or if it does not close unmanaged code (in this case a better approach is to implement the IDisposable interface). If it works, maybe a better approach is to use a new ORM once you need to create new functionalities. If the project needs a refactoring for optimization purposes, the change needs to be applied in the bottlenecks, not the entire code.
There is a lot of discussion about the topic. A good recommended resource is "Working effectively with legacy code" by Michael Feathers, or "Getting Started With DDD When Surrounded By Legacy Systems" by Eric Evans.