Because they don't want to pay the price? Because if there's enough infernal interference the gods will step in with their own powers to counterbalance and vice versa? Perhaps that doesn't happen because of mutually assured destruction? In many stories, people are pawns to greater powers but the greater powers have their own agenda.
Sure, but SOMEONE has to be willing to pay the price, otherwise warlocks would never exist. And again, this is an extremely common folk tale trope where the kingdom or local lord has a deal with fairy or spirit forces.
Also, sure, maybe the Fiends won't get a lot of traction. That does nothing to stop the Archfey. Celestials, Genies, ect ect ect. Not all warlocks make deals with demons.
What mutually assured destruction? No one makes a deal with a ruling family because then everyone will try and kill each other? Have you LOOKED at Outer Realm "politics" all it is are the various great powers trying to kill each other. And there are dozens of stories of corrupting those in power towards their agendas. This one just doesn't make sense.
I have an island kingdom that does that. But how much interbreeding can you have before you have serious issues? How strong is the inheritance over the course of generations if you don't keep it in the family?
Why do you need ANY inbreeding? It is a magical talent. As long as you are a direct descendant you get magic. No inbreeding needed at all.
We even have examples of this in DnD, with the 4e Tiefling curse, where any child of a Tiefling and any other race is a Tiefling. This is again, VERY common.
Clerics get power based on serving a god. Depending on campaign, the gods may or may not favor any specific government.
Sure, they may not depending on how the world is structured.
However, many DnD worlds are structured with the Church acting in political matters and being a political force. In those settings, why would the Gods settle for being merely a secondary power in the structure instead of the primary? Why would the Gods NOT choose to bless a chosen country of their followers?
While your nobles were learning that, the people who ultimately pull the strings have been plotting and studying courtly intrigue. Being a successful politician is it's own skill and requires significant training and dedication. Being a bard is, in large part, being an entertainer. Kings aren't entertainers they get entertained.
Who says that "my" nobles didn't learn courtly intrigue? I didn't pick those examples out of nothing. The nobility in the real-world learned history and the art of making music. This was seen as a highly important skill during certain governments.
If they are learning history and music, why not take that extra half-step into fantasy and have them learning bardic magic? That is tied to the fundamentals of history and music. This doesn't take away from their courtly training, it is part of it. Unless we suddenly decide that this takes far too much focus and leaves them politically bereft... but then martial training for knights doesn't do the same? It becomes a bit of special pleading.
How many of today's leaders could defend themselves in combat? A kingdom is not an individual, a king commands an army. Few rulers outside of very small kingdoms ever picked up arms and even then it was more of a token presence to inspire their followers than anything.
Becoming a wizard or other caster requires commitment and sacrifice. Being a leader the same. Some people do both but being a leader is completely different from being a frontline combatant. So yes, sometimes the ruler is a wizard. Sometimes they're a warrior. Sometimes, I would say most of the time depending on the setting, they're just a politician.
Today's leaders don't matter, since the DnD setting isn't a Modern world.
How many great leaders of the past were Warriors? Not even looking it up I can think of
Julius Caesar and Augustus Caesar
Alexander "the Great"
Genghis Khan
Napoleon Bonaparte
Richard "the Lionhearted"
Oda Nobunaga and Tokugawa Ieyasu
William "the Conqueror"
Constantine
I mean, I could go on, but this kind of makes my point for me. Heck, even in the "modern day" there have been 29 of the 46 presidents of the United States of America that have had military service records. That is over half.
There is obviously not a one to one, and it changes depending on the setting, but there have been far and away enough examples of warriors and military men ending up with political power to make it a decent assumption that it probably happens. Yes, the strength of a kingdom is not measured in the power of a single individuals ability to kill another individual, but that doesn't prevent the inspirational aspect of having a warrior-king who you know has conquered other warriors through skill and strength. "Strong-man" politics are a thing for a reason.