Here we go, back to what I'm good at: Worldbuilding using real-life historical models.
Part of the thing to realize here is that real-life titles are confusing as all get-out because they evolved over time. So it's not actually that unusual to have Empires ruled by Kings, or Kingdoms ruled by Princes. It happens surprisingly often. Modern usages of these terms gives the impression that noble titles are very fixed and specific and slot into a clearly defined hierarchy, which is about as far from the truth as you can get.
Let's start with the idea that the Crystal Empire as a name is likely inaccurate in the same way the Kingdom of Equestria is inaccurate. The Crystal Empire is a single city making it a pretty poor empire, and using modern naming conventions it should be the Principality of Equestria as it is ruled over by the Princes/Princesses/Principals of Celestia and Luna.
In real life there are currently several Principalities still in existence that we could look at for inspiration: Monaco, Liechtenstein, Andorra, Catalonia, and Asturias. Interestingly the Principality of Andorra is reigned over by two co-princes.
Normally this would be enough, and we could use these small nations for models for Equestria. However, that would ignore the fact that the term Prince has other meanings and usages that many people are unaware of. These other meanings lead to far more interesting places, including possible direct ties between the Kingdom of Equestria and the Crystal Empire.
Prince originates from the Latin Princeps, meaning either ‘first to seize’ or 'first citizen' depending on who you ask. Basically Prince is a generic term that can be applied to any ruler. It’s still used that way in the Catholic Church, as the Pope, Cardinals and Bishops are all referred to as ‘Princes’.
In most of history titled nobility (Kings, Dukes, Counts, etc.) were referred to as ‘Princes’ when their exact position in the hierarchy was considered irrelevant, or was unclear. Mainly because in Europe the hierarchy wasn’t as fixed as people seem to think now-a-days. In reality a Count could outrank a Duke due to seniority, wealth, or where exactly the title came from. A Baron owing direct fealty to the Emperor could outrank a Count owning direct fealty to a King who owed direct fealty to that same Emperor. The titles themselves tended to all mean the same thing (‘leader’) in a riot of different languages, all getting smashed together when the various countries invaded each other. So ‘Prince’ was just easier to deal with as a generic term.
This points out an interesting thing about Prince Blueblood. The original intent was that Blueblood would be a Duke, not a Prince, but Hasbro supposedly insisted on the change the same way they insisted on Celestia being a Princess instead of a Queen. With the preceding information in mind, it is entirely possible Blueblood *is* a Duke, but is being referred to as a Prince using that older definition. Same with Celestia. This satisfies both sides of that particular debate, but again there is farther we can go using historical models. First a sidetrack about noble pseudo-relationships.
Now, another thing that can be noticed is that all alicorns are Princesses, and it is implied that it is by definition. We know of five official alicorns in the show, all of which are or were Princesses: Celestia, Luna, Cadence, Twilight, and the unnamed princess who was victim of the love potion in Hearts and Hooves Day. I have an odd thought about that last alicorn and her relationship to Celestia and Luna, but I’ll get back to her later as I have enough thoughts around the nature of alicorns to make up a blog post of its own.
In any case, using Cadence and Twilight as examples, and pulling information from the Twilight Sparkle and the Crystal Heart Spell book which may or may not be canon depending on who you ask, and seeing Rarity's reaction to Twilight's transformation, we can infer that alicoronation is rare enough that most ponies are unaware of the process, but does happen often enough for there to be a need for Celestia to formalize the relationship between herself and these younger alicorns. And so she automatically adopts any new alicorns as her ‘neices’ or ‘nephews’ simply to prevent any political issues from arising. As official relatives of the reigning monarch, these adoptions confer the generic 'Prince' or 'Princess' title on the adoptees, protecting them politically by giving them status without necessarily giving them any real authority.
However, why was Blueblood referred to as a nephew of Celestia as well? He’s not an alicorn, nor is he the son of Celestia’s sister or brother. As far as we know, Celestia only has one sister, and I doubt Blueblood is Luna’s son.
There is another explanation. Old European nobility tended to call each other cousin, even if there was no blood shared, in order to cement their noble status via fictional relationships. That and large chunks of European nobility *were* cousins due to inbreeding, but let’s give it the benefit of the doubt there.
Which means that Blueblood as one of the top nobility in Canterlot would want to establish a tie to Celestia, the ruling Princess also currently of Canterlot. However, as an effectively immortal alicorn at least a thousand years old, Celestia is a bit of a reach to call ‘cousin’. But Cadence, as a young mortal alicorn with an assumed noble rank, isn’t that much of a stretch. In the convoluted logic of nobility, as Princess Cadence is niece to Celestia and if Blueblood can call Cadence cousin, that makes him also a nominal nephew of Celestia and cements his claim to be called ‘Prince’.
This is all airy-fairy nonsense, but that’s the way nobility actually worked. It’s all politics, and talking a good game.