There are two types of crossovers. The DC Presents/Brave & Bold team up story, which I would list the JLA/JSA team ups under. These 'crossovers' tend to be less than Earth shattering in their effects on the characters but do occasionally suffer from bad characterisation, mis-use of powers and so on. The Legion's re-introduction was in one of these crossovers called 'the Lightning Saga' but even that suffered with odd characterisation - the Wildfire/Red Tornado thing and so on.
If I'm not mistaken, Crisis on Infinite Earths was DC's first of the other crossover. The Corporate - universe affecting everyone involved - mega event. I loved CoIE but the results (Supergirl, Flash even Kid Psycho) were traumatic at a time when one death was big news. The later ramifications of the Byrne Man of Steel knocked the guts out of the Legion (and I suspect Paul Levitz) for many years.
Since CoIE we have seen Legends, Zero Hour, Infinite Crisis, Final Crisis, the crisis after Final Crisis (Blackest Night) etc etc etc. Each of these has had to top the previous for level of threat and shock value. Is anyone really shocked now when Star City is destroyed. After all it is not to long ago that Coast City went the same way. Having the Legion shoehorned into a 21st century crisis adds no value to the story or to the Legion. It may get a few readers saying wow that Wildfire is cool I may pick up an issue of Legion and check it out - but they will be few and far between I imagine.
So for me it's an odd team-up - yes. Mega crossovers - no.