Phantine Air Corps
In case you haven't picked up on it by now, the Imperium is full of such heaping amounts of stupid rules that you could write for millenia and still only record a fraction of these fucked up restrictions. One that does make some relative sense is that the Imperial Guard and Imperial Navy should be kept separate. After the Horus Heresy you can't risk another self-sufficient force (justifiably) rebelling against the Imperium.
Enter the planet of Phantine, which had an issue; all their population is forced to live at the peaks of their homeworld. This meant there was a problem for the Imperial tithe, since Phantine PDF forces were primarily pilots. Deciding they were already worse hypocrites than most popes, the Imperium decided to disobey the rule that the Imperial Guard shouldn't have an air wing. While deploying them with a dedicated force of drop-troops, the Departmento Munitorum soon revealed their newest regiment. The Phantine Air Corps had been formed.
The question of why the Munitorum couldn't just modify their tithe to providing Imperial Navy pilots instead of Guard regiments goes unanswered.
Why This Was Hated
It's already bad when neckbeards find out their favorite armies are getting changed. Imagine how the Phantine were received by the Guard and the Imperial Navy. For millenia, the Navy had been the go-to force for atmospheric transport and air superiority. Now there was a Guard regiment to take on that role? Never mind that the common guardsman is probably pissed at the Phantines in their nice personal aircraft as they're forced to slog through the mud, blood, and crud that is a 40k battlefield.
This of course means that the Phantines are pretty much the red-headed step-child of the Guard, even when it's obvious that they're probably one of the more useful regiments in the Imperium.
Phantine Skyborne
The Phantine Skyborne are some of the rarest sights in the Imperium. With less information than the Sable Swords or the Segmentum Pacificus, they are perhaps THE most unknown regiment in the imperium. Heck, even regiments like the Ritterghast or the Janiverden tunnelrats have some mention in recent codex's.
The Phantine are typically comprised of the pilots of the Phantine air corps. They function much like paratroopers or SAS commandos due to the extremeley high altitude of Phantine making every male about the age of 18 7 years old an RAF pilot IN SPAAACE. From what we don't know, we have not seen countless regiments fall in some doomed infantry advance in some desolate corrupted world which means that among the guard, likely due to their pet grav chuts, they are among the more well trained and managed regiments in the Imperium- no small feat but then again no large one either.
Why They Aren't Common
Have you fucking seen the prices to buy Imperial fighter models?
Why They Should Be Common
The great part about the Guard is that it's about the common soldier in the face of overwhelming odds, and even in the darkness of 40k this definitely extends to the Phantine. They're the same bog-standard humans as the Guard on the ground, facing down Tyranid flying hives, Eldar super-fighters, and Orks guzzling jet fuel because they can. The Phantines are the pilots up against the most overwhelming odds, facing death in the skies knowing that their efforts protect the ground forces to do their jobs without being bombed to hell. To attack the enemy behind the lines with precision strikes on vital points and fortifications. To face the same horrors in the sky as their brothers on the ground with little more than their wits and reflexes and a jet strapped to their ass. So that when they land and see that their efforts allowed others to succeed, they may know they are just as much Imperial Guard as any other in the service of the God-Emperor.