In the "old days", some IC's were in these nice round, metal packages, like this:
They are now, somewhat non-existent (ok, now I said this, some posters will show links where they are still being made
).
So they (DIPs/DILs) probably are going to somewhat gradually fade away.
But they have been around for a very long time, so I expect DIP to remain somewhat available.
It is already very difficult to get at least some of the latest op-amps in DIP packages, in my experience.
Almost no Arm microcontrollers are available in DIPs.
As the specifications and frequency increases, other (non-Arm) MCU, also get increasingly rarer, in DIP format.
tl;dr
I think DIP has already disappeared a lot. New chips tend to not be available in DIP format, these days, with some exceptions, such as some PICs.
***EDIT: Chips with lots of pins (e.g. > 28 pins, but especially > 40 pins) and high performance (frequency) parts, tend to not be available in DIP format. But I agree that small/simple low pin count IC's, such as LED drivers, logic and some other stuff, is still available in DIP format.