@Sjogre
Why does she want a replacement? Because she’s been walking the Earth for better than 1,000 years. Because every being that could possibly relate to her has gone insane (I’m thinking of Luna and Discord) and needed to be sealed away for the good of her people. Because when those beings were healed of their madness or reformed, she had precious little to do with it.
Why does she insist on a god queen instead of transitioning to mortal rule? Because people fear change. They’ve had more than 1,000 years of rule by immortal god princesses, if Celestia just up and said one day “well now we’re a democracy” I’d give it a week before the situation devolved into sectarian infighting. You point out that until Luna was sealed up she shared the throne, but after luna was sealed up it was 1,000 years of her ruling alone. Think about the time span involved. The only creature alive to remember Luna being co-ruler of Equestria is Celestia herself.
Also you claim that rule by immortal is the exception not the rule, even in Equestria, and I think you’re not quite thinking about the time line properly. 1.000 or more years isn’t a huge chunk of time on a geological scale, but it is almost incomprehensible on a historical scale. Sometime after the third or fourth generation of ponies born with immortals holding supreme executive power its going to start seeming ridiculous to ponies that other civilizations don’t have immortal rulers and the exception becomes the rule.
In fact you’ve actually just made it more interesting… she leaves power in the hooves of a pony who has to share custodianship of the most powerful magical force in Equestria with five other ponies. What if the plan is to introduce a republic to ponies gradually over generations, she just hasn’t found the suitable candidate yet.
As for why ponies would prefer a single, eternal ruler, study human history. Monarchies are all about a single ruler whom the people believed to have power and authority by divine right. How much more powerful would the claim to divine right be for an eternal princess? And who’s to say she even claimed it herself? We could be looking at a
Life of Brian type situation where people will see her as divinity no matter what she does or says.