Long ago, before Stellar abdicated the throne, he did in fact have an admirer/pseudo rival.

Solar Wisp is the son of Moondancer and Starlight. He was born with a lot of raw magical power and his shitty elitist behavior was almost encouraged [at least to an extent].
Not many unicorns could match Solar's magical prowess. The exception being Stellar Rayon, of course.
Stell is a shy boy who spent a lot of his time exploring pastoral magic. However, he was born magically strong and raised to be the best of the best. Solar should have seen him as a rival but ultimately likes Stellar for what he signifies. If they were to marry, Solar would be royalty which is too tempting to avoid.

Stellar was tasked to beautify a meadow outside of Ponyville for Princess Celestia's wedding. Solar can't help but drool at the purple unicorn's magical display!