Valve and Bethesda did more than just allow the script extenders on the work shop. They worked WITH the script extender team to get it to function with valve's bootstrap program. I don't know if a script extender will be included or not on xbox but I have no doubt Bethesda wants to and will probably put "some" work into trying to do so.
The problem with the DEV trying to make their own extender is the very nature of a script extender. Each new function can create bugs. If the DEV has no use for a function but throws one in anyway it is very hard for them to debug that.
AND building a powerful library is very much a slow process (years) of mod makers trying to do "stuff", find they cannot then ask for a new function, new one is made by a very elite team of programmers, mod makers use the new function out the "wazoo" (find bugs or confirm it works with all the other complicated systems in the game) and so on.
It would be hard to "guess" at what mod maker's would want and get the same great results as one that is build over time with a lot of input from those of us that actually use the new functions.
That said I REALLY hope Beth does try to make their own extender. They could look at past extenders or even talk to the extender team for suggestions.
DEV made and a user made extender TOGETHER would be wonderful for modders.
By the way I read an article about how you will mod FROM in the game on consoles. The impression I got was that it was part of the game not a separate program. But I could be wrong. If that is really the case that could explain the 8gb requirement for the game.