One of the biggest problems with using paratroopers besides the limit on airlift, and why they’ve just been high-readiness/at-least-theoretically higher skill infantry in real practice, is the cost-benefit with their operations. This is very tricky.
The Practical Reasons
Apart from situations where there just is no other way to move in quicker (ie, over bodies of water/other gaps), airborne landings, particularly on a very large scale, have faced the issue of either being unnecessarily risky and complicated for the task at hand or simply being too weak to accomplish anything (especially in a situation where everyone has a lot of heavy forces).
The impression I’ve gotten is that anything bigger than a company-sized landing force is dicey, and anything bigger than a battalion is really, really dicey. Yes, if everyone had giant Mi-26 sized helicopters and/or the landing forces had mechanized equipment of their own (ie, BMDs/Sheridans) it would help, but only somewhat.
The Literary Reasons
On the other hand, the literary reasons for big airborne operations are obvious. Just look at Band of Brothers, to say nothing of considerably more obscure works of fiction that range from Marching Through Georgia to Northern Fury H-Hour.
- They’re big and dramatic all by themselves.
- Because they’re often centered around (seemingly) important targets, it makes the actions of the protagonists look bigger.
- Because airborne forces are inherently limited, it means drama can be maintained against a seemingly weaker opponent (a pretty extreme example of this is Marching Through Georgia, where the Draka are otherwise utterly superior to their opponents and paratroopers against a panzer force are the only way to have something even slightly even).