So I have a theory/headcanon about the laurals in Hades.
As we know the royal family, Hades, Persephone, and Zagreus all wear the flaming laurals.
But before Persephone joined them back as their queen, she didn't.
This leads me to believe that only royalty can and do wear laurals around their heads.
"but shabby!" You may say, "Thesus wears blue ones!"
And yes! He does! Thesus though was the king of Athens. And is refered to in the game as "king" several times, so although they're not flaming, he does have a set of laurals to show his station.
"what about Asterius though???"
And I'll admit. This is more of my own head canon here. Asterius does indeed wear laurals, but I think they're because they were a gift from Thesus. Wether they're a gift to show close friendship and companionship or a gift of lovers is entirely up to you.
But now we get to achillies and patroclus.
For anyone who doesn't know, patroclus was born a prince, but at the ripe old age of 9 he was exiled and lost that title. He has not been a prince since he was very young.
Achillies however never lost that title. He was born a prince and died a prince. He should still have his laurals and yet we see it's the opposite in game.
I truly believe that after Patroclus was slain, achillies removed the laurals from his own head and put them on patroclus's. As a sign of devotion, of his love. There would be no one else in achillies life who would be worthy of wearing his laurals, of being his partner and lover.
When their bodies were burnt and buried I think patroclus was still wearing the laurals and took them into the after life with him.
Being the only gift he has from achillies with him, he keeps them on knowing the symbol of love and devotion that they are. Taking them off would mean finally moving on from the love they had for one another.
Achillies likewise refuses new royal laurals. His deal with Hades means he's now a servant, not a prince. And replacing the laurals he gave to patroclus would be too painful. You can't replace the love you have for your soulmate afterall. That's not something you can just move past.
Edit: if anyone wants some angst to go with this hc, I've wrote a small accompanying fic