Do I look bothered?
The Big Corporate lever is not so much single-point-of-paperwork as scale and resources to sort out problems. Government beancounters hate writing off an unsuccessful project and somebody cocking it up is a powerful reason why gov't projects fail. By getting in bed with a Big Boy, you convince yourself that they will be able to throw resources at any cock-up to sort it out and meet your delivery targets. Cost escalation then becomes a blame game between the legal teams, i.e. Somebody Else's Problem. Small fry just don't have that kind of backup resource to call on.
Of course, F/LOSS licensing blows that corporate stitch-up out of the water, but that requires a change of procurement policy, nay even a rewriting of the Preferred List and Approved Catalogue, a painful process which government departments are singularly unwilling to carry out.