Possible Story Ideas

[Neoteny]

I'm pretty sure it has it's own mind as to what to do.

In the outlines it has Zion/EPN saving it from an Oligarch stronghold just because it's Trinity and stuff, not because they think they can use it for anything.

She decides herself to integrate with the source/destroy the oligarchs/save the Machines. The programs got free will now, it doesn't matter who holds it, it makes up it's own mind (especially if it was strong enough to lolpwn Wright).

It does if the people holding it have the capacity to contain it (i.e. the Oligarchs, the Machines, possibly the Merovingian)

Granted Zion doesn't have the force necessary to contain it, but the emotional side of Trinity might not want to go ahead and suicide throw itself at the source just to block/kill the Oligarchs it barely knows.

I think you're giving the program a little too much credit. Sure it took out Wright, we don't know how, and we don't know why, and we also don't know if the program knows either of those things.

If it has the mind of Trinity in it, I'd assume it to be rather confused. And that confusion adds depth where even the most fruitful suicide makes it just another villain of the week type character. Certainly, it could make up its own mind to do such a thing (provided it isn't captured by any force prior to that happening), but there needs to be a rationale for it (which would encompass at least a subchapter or two, if not a full chapter of storyline development [alongside other things, of course])