The legality of disinheriting an heir is somewhat unclear in the text, which isn’t at all made better by the cases where an heir is simply passed over or has another named ahead of them without a legal disinheritance. To give a few examples, Randyll Tarly mentions that he has “no cause to disown” Sam but since he also wouldn’t allow him to have Horn Hill, he terrorizes him into renouncing his
rights and joining the Night’s Watch instead. Tywin Lannister, whose hatred of Tyrion is infamous and who makes it very clear that Tyrion will never get Casterly Rock, also does not drop him from the succession until after Joffrey’s assassination and Tyrion’s conviction. Similarly, neither Aegon the Unworthy nor Aerys II did deliver on their threats of
disinheriting Daeron II and Rhaegar respectively even though they blatantly favored Daemon and Viserys and hated their eldest sons. Of course it’s worth mentioning that Aerys did
eventually

disinherit baby Aegon after the Trident but that does not tell us much considering the unique circumstances of that from Aerys’ uncaring view of law as something to abide by, to the rebellion that rejected the Targaryens as a whole so who cared about their succession. To return to a more current case, we have Robb’s will in which he might have disinherited Sansa, but he might have also only named Jon ahead of her in the line of succession rather than disinheriting her completely.

So, I’d argue that it’s fairly hard to disinherit an heir – specifically a male one – otherwise we’d have seen a number of disinheritances in the text. The level of acceptability seems to depend on legal or political causes. To go back to Randyll’s words, it appears that a lord
needs legal cause
to disinherit his heir – if the heir committed a crime for example, like in
the case of Tyrion being condemned for kinslaying and kingslaying. It might happen if there’s enough political support for it, like in the case of Aegon V giving Prince Duncan a choice between the throne and Jenny of Oldstones (though Duncan ultimately abdicated), or if Robb did disinherit Sansa to prevent Winterfell from going to the Lannisters. The heir can also abdicate voluntarily like Prince Duncan the
Small, or “voluntarily” like Sam.

That said, this does not exclude possible ways to get ride of an heir through some extreme measures. I mean, a lord can always have an unwanted heir killed or force them to join the Night’s Watch like Randyll Tarly did with Sam but not only would that require a person willing to do that but it can invite war since a male heir, especially a prince, is likely to have supporters who would fight for his rights. In the case of a royal heir, it becomes harder to force an abdication, whether via the Night’s Watch or not, without a legal cause to justify it. After all, if the king can just send his own heir to the Wall for no crime, his lords might have cause to fear him doing it to any noble who displeases him. Now, technically
a Great Council can be employed towards getting a consensus to set a
prince’s claim aside, but I don’t imagine the prince in question would
just wait politely for that to happen, and the lords probably wouldn’t agree to setting aside the claim of an adult male male-line heir without a compelling reason. A king can also simply name a younger son as heir ahead of his older brother in defiance of succession laws, but considering that the last time a king used royal prerogative to name his heir led to the Dance of the Dragons, his lords aren’t likely to accept that. Too, leaving the line of succession
to be decided arbitrarily by the king can lead to heirs being disinherited for any numbers of reasons that do not
necessarily have anything to do with being unfit to rule.

Imagine how Aegon the Unworthy would have loved the opportunity to actually disinherit Daeron.

Moreover, to address your specific examples, keep in mind that Aegon’s unworthiness wasn’t yet clear
to the lords of Westeros during his father’s reign. He was still young
and handsome and charming, a veteran of the conquest of Dorne, and the complete opposite of the aging financier
Viserys

and the scholarly physically unimpressive Daeron (who would be the one Viserys replaced Aegon with, not Aemon. The Dragonknight was a Kingsguard sworn to hold no lands or titles). While Aegon’s hedonistic nature was apparent, Westeros isn’t a society that condemns men for sleeping around and most of Aegon’s dubious relationships happened with women the average Westerosi lord doesn’t care about. So with his tyranny yet to emerge and his charming and generous personality gaining him popularity, Viserys would have a devil of a time getting his lords to accept his decision to pass over Aegon, and Aegon’s faction would start a war over the succession. As for Aerys and Rhaegel, the two princes only came that close to the throne in the wake of thee unexpected deaths of Daeron’s three immediate heirs. Even after Baelor Breakspear died at Ashford, there was no reason to think that Valarr and Matarys wouldn’t sire heirs and no one could have predicted the Great Spring Sickness.

As for why Randyll Tarly chose the Night’s Watch rather than the Citadel or the Faith for his eldest son, Sam has the answer for that.

 “My lord, my f-f-f-father, Lord Randyll, he, he, he, he, he … the
life of a maester is a life of servitude. No son of House Tarly will
ever wear a chain. The men of Horn Hill do not bow and scrape to petty
lords”

While the Night’s Watchmen also take a vow of service, it is still a military order that is built on the performative masculinity that Randyll favors and understands. They are the black knights of the wall, to hear Sansa tell it though Randyll certainly wouldn’t go that far. Still, a military order that has anointed knights and exists for warring reasons, in the far North where Sam would be out of sight and out of mind and bound by vows that forfeit his life if he thinks to desert, is exactly the place Randyll would choose for his disappointing eldest.