One of the key things that differentiate Agile from Waterfall is iterative development. There's also incremental building and the presence of time boxes.
Agile is a framework which, as you mentioned, is very lightweight. Over time people have felt the need to standardize how things are done for many reasons including 1) being in a heavily regulated industry and 2) being new to Agile and wanting to provide clearer guidance to the teams to try to contain the amount of projects that fail when the organization "flips the switch" to go Agile. This thesis is supported by information on this page.
blogs.versionone.com/agile_management/20...t-scrum-methodology/
DSDM, AUP, and other heavyweight practices make up a smaller percentage of methods being used today than they did in 2006 according to the page cited above so I strongly believe they're used as "training wheels" and then the teams are allowed to move towards more lightweight approaches where they have enough data from past projects to implement best practices, stay true to Agile, and change what wasn't working.
The Agile Manifesto outlines the MINIMUM requirements for a methodology to be Agile. Building more structure around it as is the case with DSDM still makes it Agile as long as the core principles aren't violated.
