The problem here is that you don't understand the nature of the Empire at all.
It is build entirely on the concept of Slavery. There is no middle class. You ether do hard backbreaking work under contract to pay off debts or you're riding the high live enjoying those luxuries that may put you into debt. The Empire wages war with genetically modified slave army soldiers. It is highly resistant to change as it took over a millennia to even reverse the original decision that the position of Emperor could be passed down to sons only.
Aisling stands against everything that is the Empire. Her position is not popular.
Not to mention this is the Empire we're talking about. Where a minor group successfully assassinated the previous Emperor for being too "progressive" in reformation in an attempt to remind the Empire of what it is. While he was a reformer, he was still the Emperor and this outrage led to the Empire, playerbase and all, to come down in a fury that hell hath no.
His successor, Arissa, was put into power by the senate because her views align with what the rich and powerful believe the Empire is. (Not to mention it keeps them rich and powerful.)
If people are willing to assassinate the Emperor for allowing Arissa to take the throne because of her gender, what makes you think they're willing to allow someone with even more radical reforms to continue living? Very few are wiling to openly do away with her but when an opportunity like this arises... don't hesitate to think for a second they wouldn't take it.
The Federation is not going to care because the Feds and the Empire have been enemies/rivals since the dawn of of the Empire. They might even send in Black Ops and have her die tragically in the crossfire.
Basically, you couldn't have picked a worse target for demanding ransom. The one with the smallest support base in her own domain where the overwhelming majority would love to see her offed and the rest of the galaxy will shrug it's shoulders or see an opening.
So yes. This viewpoint is entirely 'normal' given the way the Empire operates. Anything that shakes up the Empire in such a radical way like a highly profiled individual meeting a tragic end is a desired outcome.
Now if you'd gone after ALD or Patrius....
Honestly you need to consider the allegiances of your audience. As a Federation Admiral, your "Lose/Lose" situation is actually a "Win/Win" for me. It means you don't have enough of a following to be a credible threat to my operations AND it removes a high profile target of an enemy faction.
Hell, even your "Win/Lose" is a "Win/Win" for me. People will be too focused on you that I can quietly build up a force without notice to counter you AND just sit back and watch as the Empire takes a hit.
In the Inverse. Your "Win/Win" is actually a "Lose/Lose" for me because now it means you're a threat I have to contend with alongside everything else and the Princess remains a thorn in the side of the Federation. So I should seek to actively prevent that scenario.
After all, you did say that a "Win/Win" is the best outcome and the best outcome is that both you and the Princess die tragic horrible deaths.
Excellent analysis, it seems that you've put extensive thought into your response. I can't say that I've had a troll-post work this effectively on someone for quite some time. Hahahaha.