I don't believe that mixing, was the main issue, the fact that, new foreigners just didn't want to identify as a Roman. Understandably to some extent as the Rome at the end of their empire was a far cry from the start. The meritocracy was all but gone, debauchery was the hobby of the rich and the military was in a deadlock. I'm certain at the rise of the roman empire, foreign powers where proud of the goal of becoming roman.
But towards the end, just like today, because the people never saw the rise, the power/class divide and the lack of good faith. Foreigners would see this as a power that was unearned, unworthy and unfair. Why would they want to be a roman, a people that doesnt deserve what they have...
I believe for a civilisation to succeed, the foreigner has to want and believe the ideals of the country/civilisation they inhabit. The goal of integrating into the society whilst keeping some culture and integrating it where the society sees fit. A foreigner that doesn't want this doesn't respect the place... and when that happens, they can form groups that follow ideals against the government and society... leading to an easy divide when the opportunity arises.
So yes, foreign mixing can be a boon, but only when they want to integrate and share the values of an ideal they look up to :)
Else it's a liability.