The reason for that lies in the fact that all possible paths must be explored and then individually invalidated. This becomes a problem which grows as the factorial of the number of BGP speakers, and results from avoidance of loops. Essentially, this means that in the extreme, BGP may not converge at all. So far, we are saved by BGP policies, and several BGP timers which put a bound on some of the behaviour. However, with an ever growing Internet, this becomes more and more of a problem.
Conclusion is that it has no influence.
Yes, it would bound some of the announcements. However, the worst case scenarios don't really occur in real life. Some people in the room have been affected by wrongly set dampening parameters. This was also the reason for ripe-178. 2 AS's connected in 4 places, a withdrawal would travel 4 times between the AS's.