Agreed, agile seems the only way, but does indeed require experienced managers. A lecturer once pointed out that business/normal people would always expect some kind of point estimate, they are never satisfied with some kind of distribution or interval. Personally, I would say that this is even more sad than that: the point estimates are always taken at the extreme values, which ever suits the person wanting the estimate more, never the average value.

Of course, all this leads to bad blood between techies and business side: how long will it take? -> probably about 3 weeks, but this requires using a library we haven't used before, so in the worst case even 2 months -> what? so long? get it done in 4 days, this is required the next week -> no, that's not really possible -> make it happen -> it happens and it either sucks when it's delivered at all, so the deadline gets extended anyway to iron out all the bugs or it causes lots of problems in the future.