And this is where I think you do not understand the situation.
Henrietta sparing Louise is BAD.
Because it confirms the "Close relations" of the Valliere and the crown, not only making the Valliere a high priority target (to destroy, manipulate, or weaken), even moreso than before, as well as undermines the strength and powerbase that the princess has built up over the duration of her term.
Karin "knows" that Henrietta is a weak queen. Every noble "knows" that Henrietta is a weak queen. A queen so afraid of mages she dismissed her 3 personal contingents of mage gaurds and surrounds herself instead with "Commoners". She's Too afraid to use the very gaurds they have provided for her specifically. And everyone knows it.
Make no mistake, the execution of Richmond is not a sign of strength, but weakness. A queen so weak she has to resort to putting herself on the line (kidnapping herself) in order to find and catch a traitor. There was no assassin making an example of her political enemy, or brash unbased execution. She had to put herself in danger, all while pretending to be, and using a literal army of commoners to apprehend one corrupt judge.
Henrietta "going easy" on Louise because a) Everyone knows they're friends, and b) She's a valliere, and the valliere are "in bed with/favored by" the crown, or at least, Seemingly so, is probably the worst thing that can happen to both the Valliere and the crown itself.
Remember, at this time (Even after Richmond's death), Karin and Duke still call Henrietta a weak queen. And these are her supporters! Not only that, but look at her interactions with Karin when Henrietta's trying to call her off: the "queen" is basically a ball of quivering nerves, barely able to articulate her commands. There's no way Karin would take that seriously.
Frankly outside of knowing Louise was a Void Mage, allowing it to go through is a BAD IDEA, as Germania was Tristain's ally against Albion. They never said anything about Gallia. Not only is Tristain weak and completely unprepared for a second engagement, what makes matters worse is that Henrietta is welcoming Louise back with "Open Arms", It's like asking Gallia to declare war and attack. Karin sees more of the situation politically than you think. After all, her quote:
"She is your and my daughter! It has to look strict! A long time from now, when you're looking back, you'll see her being raised up wrong because of your selfish whim!"
At the shout of his wife, the duke instinctively ducked his head.
"S-Sorry!"
"Our family is important, our daughter is important as well; I don't want to pass on either. That's why the "Heavy Wind" will give the punishment to our daughter. Her Majesty will see."
She has to make it look strict, or else everything would be pinned on them. It's not a good situation. And it doesn't matter the truth either, but how it looks. And it doesn't look good.
If Henrietta came out and said "It was my idea all along, it was all a covert op, disguised as treason!" Then your argument would hold water in my eyes. But in-verse it's just a weak queen saving a childhood friend, and putting everyone even moreso in danger.
I mean look at this:
"You should not be violent! I came here to deal with Louise's punishment myself. Because I am young, at first I was resented. However, I thought about it a lot. Though Louise passed national borders certainly without my permission… I am also worried about it as a friend too. Just a strong reprimand will do, I do not intend to give a violent penalty."
"Your Majesty, your words are kind, and you feel regretful. However, Your Majesty's royal prerogative is of the sacred non-aggression given by the Founder. Thus, you have to protect the laws of the country promulgated in that name, too."
The way Henrietta tries to deter Karin only makes it even more prudent for Karin's punishment to be severe! If henrietta HAD her act together and DID NOT look like an unsure, weak, young regent then what you said would apply.
But right now. you can see that even Henrietta is hesitant to forgive Louise.
This is not HoS, where henrietta's strong and in control. Louise DID commit treason, even going against being imprisoned by Henrietta. Henrietta also DIDN'T let Louise escape. She is THOUROUGLY AGAINST this plan. Don't confuse the two verses.
This is basically on par with letting an rouge agent breaking out of CIA custody, having it blared all over the international news, then allow him to bomb/destroy, say, England's capital and then kidnap a high security target, and then be allowed back into the united states, with great fanfare and celebration publicly, along with taking custody of the target, all while pardoning the rouge agent for treason and tresspass while refusing to allow the target back and the agent to stand justice.
Make no mistake. Poilitically speaking and honestly speaking from the numbers, Louise was wrong. It makes you feel nice, morally, to save a damsel in distress, a princess locked up in a tower guarded by a monster. But make no mistake. What the heroes did is Wrong. Unabashedly Wrong. Treason, sedition, you can even put a spin on it and call it "terrorism" if you're a warhawk. Louise, for all intents in purposes in the eyes of the international (but more importantly Tristainian) community, committed an act of aggression in a foreign, Neutral/ALLIED nation.
And Henrietta was going to let them off... protect them even, from the coming wrath of Gallia.
It does not add up. This is a classic example of saving one over the many.
But of course, we Know Louise and Saito were
Right because they're the
Heroes after all. They
Can't be Wrong.