When the business of shutting down land bases was active, it was not considered that easily done with conventional ballistic missiles. They're just really big things to put out of action with one 1 K blast at a time, and the vital bits and pieces can be dispersed. The infamous JP233 was designed for the job, but combined concrete-heavers with mines to impede repair. You "harden" by dispersal and repair.
When you're dealing with a system that relies on a number of critical items to work (eg runway, fuel, bomb shop, C2, maintenance), you have two options - you either concentrate them and protect them or you duplicate them and separate them. That is classic vulnerability reduction doctrine. On most airbases I'm aware of there are however, single points of failure, like fuel farms or bomb shops or the mid-point or intersections of runways. While some are hardened (eg buried fuel and bomb dumps) they are
not hardened against a penetrating targetted attack.
The issue with conventional BM was always that although they could suppress a base, they were never sufficiently accurate enough to target discrete facilities like those above. Now if people are suggesting that a BM is capable of targetting a 300m x 70m platform moving at 12m/s+ in a oner, then I'd suggest that the same weapon is perfectly capable of targeting a static runway intersection, a fuel farm, a bomb shop or the C2 bunker. Losing any one of those is likely to stop operations. The cratering effect of a targetted hypervelocity HE warhead will far outweigh that of Durandal or JP233 on whatever it hits - repair may not actually be possible in a tactical timescale.
Just as a comparison, the good old Grand Slam weighed in at 10000kg and arrived at just about the speed of sound (320m/s), which by my calcs is about 512MJ of energy, excluding the 4000kg of explosive power carried. If you assume that your DF21 presents a calling card of 1000kg at (say) 2500m/s (not unreasonable for an RV), that's 3125MJ, excluding the stuff that goes bang. Now I'm pretty sure runway repair teams aren't scaled to deal with a Grand Slam level crater easily, so I think they might struggle with something delivering 6 times the energy before it goes bang. If something like that hit the fuel or bomb dump, the effects are likely to be on the spectacular side.....
Also, although the adversary knows where the target is in the case of a land base, the defender has some options because he is not limited to the magazine size of an Aegis ship. A regional TPY-2 and a whole bunch of David's Sling missiles could give the attacker some problems.
As Orca has pointed out, there is a much more complex system required to target a BM against a moving target, which can be disrupted. For a fixed target, access to a targetting database derived from Google Maps and an accurate GPS fix might suffice.
I should have thought 150+ SM2 block VI/SM3
ready to fire in VLS from just two Aegis ships defending a small area is probably more than might be available from a theatre-level Patriot unit in the US Army. Not that it's designed to go after real ballistic RVs like DF21, nor is David's Sling apparently.
No one is suggesting carriers are invulnerable to attack. It's just that folk tend to assume that land bases are - which is a long way from the truth.