The real question is: Why do the Nerevarine and Hero of Kvatch get birthsign blessings when nobody else does?
To be clear, I'm talking about a life-long benefit based on the birthsign that a person was born under. I'm not talking about the Mundus stones or similar that either grant a temporary or interchangeable benefit regardless of what birth sign you were born under. First let's review which games have their protagonists get birthsign blessings:
Games where the protagonist gets a birthsign blessing
- TES III: Morrowind (Nerevarine)
- TES IV: Oblivion (Hero of Kvatch)
Games where the protagonist does not get a birthsign blessing
- TES I: Arena (Eternal Champion)
- TES II: Daggerfall (The Agent)
- TES: Battlespire (The Apprentice)
- TES: Redguard (Cyrus the Redguard)
- TES: Stormhold (Master Tunnel Rat)
- TES: Dawnstar (Hero of Dawnstar)
- TES: Shadowkey (Soul of Conflict)
- TES V: Skyrim (Last Dragonborn)
- TES Online (The Soulless One)
As you can see, receiving a birthsign blessing is something of a rarity, even among the movers and shakers of the Elder Scrolls universe. Before we examine those who got them, let's review what the constellations actually are.
In The Elder Scrolls Online, it is revealed that the constellations are actually powerful god-like beings named the Celestials. During the games, the constellations actually fall from the sky and take a mortal form, at which point the Celestial Serpent plots revenge against them. Eventually, they do all return to the sky.
I imagine that, like the actual gods of Tamriel, they have the power to directly influence the world, but choose to do so to a limited number of people. So let's look at the two they did influence.
The Nerevarine (the hero of Morrowind) is the reincarnation of the Chimeri warlord Nerevar and is tied to astronomy in multiple ways. The prophecy "The Seven Visions" says the following of him/her:
On a certain day to uncertain parents
Incarnate moon and star reborn.
Nerevar also went by the title "Nerevar Moon-and-Star" (which is what "Incarnate moon and star" refers to) and it's clear that the Nerevarine will be known to be born on a certain day, which is marked by the birthsign that the player chooses at the beginning of the game.
It is possible that the importance of the stars meant that the Nerevarine was blessed by whichever Celestial had a constellation that they were born under.
The Hero of Kvatch
Also called the Champion of Cyrodiil, this hero from Oblivion didn't really have anything special about them other than being the right person at the right time (pretty similar to the Eternal Champion and the heroes from most of the spinoff games).
I'm going to go out on a limb and speculate that this hero got a birthsign blessing because the Celestial associated with their birthsign knew that the Oblivion Crisis was imminent and that would be the most disastrous conflict history had ever seen, so they decided it was in their best interest to give them some help.
Either that or the Celestial was jealous that the Nerevarine got a birthsign a few years earlier (Morrowind and Oblivion take place six years apart) and decided to give a birthsign to some bloke who looked like he was going to do important stuff.
Unfortunately, this is pretty much all speculation on my part, as there isn't a clear source that explains the birthsigns in greater detail. If birthsigns are directly given by the Celestials as I speculate, then I imagine that each Celestial has a reputation for giving certain benefits and this creates the tradition of what being born under a certain sign means.
Then again, it could all very well be a random lottery and two heroes were just lucky enough to get a birthsign blessing. Without further proof, we just don't really know.