If one can get good integration between the existing language and the tool, and have the right features (not too few or too many), then that would be best. People can transfer the knowledge, and the developer can save time.
Of course, on a cynical note, not all companies may want skills to be transferrable - that would mean users can easily leave.
I imagine that many have their own languages because 1) in the beginning, they want only a few features, so a full langauge is overkill, and 2) making languages is fun (and 3, the cynical point above).
I believe Lua is a popular language in the scripting-for-other-projects space:
What do Adobe Photoshop Lightroom, Angry Birds, Apache HTTP Server, Apache Traffic Server, the Firefox web browser, MediaWiki, and World of Warcraft all have in common? They are all extensible using the cross-platform Lua programming language
In the particular example of GameMaker and Python, it's worth noting that GameMaker is pretty old (1999) - Python 2.0 wasn't even out yet. (It even existed under another name before that, but I don't know if it had GML). I'm not sure GML has always been proprietary and I can't find it - it at least used to be free to use.
(Note that as a user, you should prefer a non-proprietary langauge - GameMaker used to be free, but its 100$ now, while Python is still, and will probably stay, free.)