It would be nice if the travis-ci build page had a button that allows to merge the latest code in master to the code that are building.
Is like the button to update the branch that exists in a pull request page.
Aren’t you confusing something here? I believe Git operations are a part of, and belong in Github’s, not Travis’ UI. travis-ci.org's webhook doesn’t even have a permission to make any changes to the repo.
You should probably leave this FR at the GitHub Community Forum.