I understand how you feel, but you give it too much credit. The reason you were grabbing the big materia was SHINRA MAN BAD. The honest answer though is that whatever plan Shinra has is probably a shit one that can make things worse, so it's better to stop them.
According to a wiki "Cid doesn't want Shinra to get their hands on the Huge Materia, massive concentrations of the planet's power, and wants them for their own use to fight Sephiroth. "
You could interpret that as 'lets get this shit and see if Bugenhagen can hook us up' but honestly this is the most thought I've ever put into FF7's story, so I don't fucking know.
This is all coming from a guy who's relatively pessimistic about the remake though. Everything about the intro cinematic rubs me the wrong way, from the jerking off One-Winged Angel to even the little shit like making Aerith scared for some reason. Most of it I think stems from my dislike of Nomura, but I seem to be a minority on that.