If I read you correctly (quite possibly not) you're proposing something like the output of "mysqldump -d" be compared to some golden schema dump and then implement something like RANCID for routers such that changes in the DB schema get emailed or otherwise loudly announced and tracked vs the golden schema. I do that. A very small shell script can take care of irrelevant diff outputs (timestamps and default minimum autoincrement numbers the like)
On a side issue (kind of), something not covered in the squitch tutorial is if you git-flow then you probably should lay down some discipline that the exact name of your feature branch is the squitch change name, just to keep insanity levels down. Also I've done things like a git-flow feature branch results in a completely new test table name being created and there needs to be discipline that the test table name is "normalTableName-gitflowFeatureBranchName" or some kind of site standard. Its only kind of a side issue, in that your proposed Data Dude app probably should cooperate with git-flow workflows.
> so why the heck are we writing migrations for our DBs
Sometimes dumb indexing decisions can take hours / days to apply and kill the NAS, run the system out of storage, etc. I've done that and its not entertaining, so its less painful to do "real stuff" by hand, at least to production machines. Tend to find some hilarious scaling mistakes. Very few source code diffs scale the source code length itself exponentially or something equally naughty so its always safe to commit/pull source code changes and automerge them, not so much schema changes.