My small experience with ELT and reading makes it look like it is mostly for development. Because the data is not cleaned up like in ETL that makes me think the new application will need to adapt its queries to the old data structure alongside the new application's new data structure. And, then, eventually ETL takes place somewhere down the road, in the new database, overtime until you only have your new application, new schema, etc., the old data schema isn't used anymore. It may still be in some tables somewhere, but unused, archive only.
For something like a hospital, ELT doesn't feel right. I would think the hospital wants things cleaned up before the conversion.
Is ELT for going to a new application in a super critical life or death system?
Edit: This article was suggested, http://www.jamesserra.com/archive/2012/01/difference-between-etl-and-elt/
After reading this helpful article, one of the ELT cases for preferring ELT is:
The source database and the target database are the same
What does this mean? The same database engine or the same schema? New applications that replace 20-year-old systems don't usually have the same schema, so I do not understand.