The problem I found with methodologies is that you have to work around them. That applies to design thinking methods as well. When I was trying to use them in college, there were always discussions around whether we were using those methods correctly. The thing is, they are ambiguous - you can always get something out of them. The framework does not crash or self-destruct when you use it wrong. We got results, but were they the right results? That has added to a lot of confusion and unnecessary discussion.
The biggest difficulty is that there are many design thinking frameworks, and sometimes it can be a little bit difficult to wrap your head around them if you want to use them immediately. Methodologies are as good as the amount of thought that was given to them by a person who has invented them. You do have to think like them in some cases, and it can be a burden.