Retreating nair gets grabbed by a shielding Falcon. Sad really, because that means Marth / Sheik can easily grab it. Dair would be treated the same in that situation. Fox isn't in the air for as long as Falco is, thus preventing him from retreating as far while airborne. Because of the inherent similarities between Fox and Falco, players intuitively think its a great idea.
Fox is often better crossing up or staying in his opponent's face. His retreating aerials are not as effective, IMO.
I'm about 90% sure you can use your tippy toes to pull a Falco and get out of range of the smaller shield grabs like Falcon and Peach. You might have to start the pressure a little differently at first, but that might be something neat to explore anyway.
Sheik and Marth obviously giggle at this sort of thing though.
I'm not sure how much I like drillshines as a primary means of pressure just because even if you hit one on a retreating opponent you usually can't follow it (sucks when your dair clips them as they're wavedashing away or whatever other actions may be incurred... too many times I have hit with a Dair as they're moving away and I get the initial hit of the Dair but their WD momentum and body contortions take them out of my reach for the remaining three or so hits and I get grabbed).
I feel the simplicity of the drillshine as pressure is a limitation. I usually feel, when Fox drillshines my shield, I have an opening between the last hit of it and the Shine. I usually feel I can do actions there. Because drillshines never change substantially, it's kind of relaxing to know there's a constant. With Nairs I know they can switch up the timing or whatever to intimidate, trap, or put pressure on me but I don't feel that sort of fear with Dairs. Full jump Dair as pressure is sometimes really annoying though (even if it's not legit it's so cute and kind of counters a bunch of stuff... thank god for wavedashing though).
I also feel when I do early Nairs they're more likely to hit someone WDing through me than a Dair is but I may just be slow.
That said, I like drillshines when people are on platforms because you get a bunch of hits and you don't have to jump up with any spacing or timing like you would with Nair or Bair. You can also sometimes knock people off the platform with the multi-hit and try a bizzare awkward combo setup, although if they're super close to the edge of the platform Uair is better for that.