I don't think they're going out of style....at Christmas I found out my cousin is expecting a daughter in April; his wife made sure to mention that they'd "really treasure a handmade baby quilt" if someone "happened" to give one to them. She even made sure I knew what their nursery colors would be.
(And of COURSE I'm going to make one, or two...) They're a young couple (mid 20's) so if they're wanting a baby quilt I don't think they're going out of style.
I made baby quilts for my niece and nephew too, they're 10 and 14 now and my sister still has their "blankies". Not very well made since I had no idea what I was doing at the time but they're still (mostly) intact and got lots of use.
I think giving handmade baby blankets is one of those traditions that is going to stick around for a very long time.