[RPG] What’s the mechanical point of melee weapons’ range

No, you can't take the -5/+10 while throwing a dagger.

Thrown: If a weapon has the thrown property, you can throw the weapon to make a ranged attack.

Throwing a dagger is a ranged weapon attack, so the first two benefits of the Sharpshooter feat will apply. However, the third benefit doesn't require a ranged weapon attack:

• Before you make an attack with a ranged weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack’s damage.

It specifically requires that you attack with a ranged weapon. The thrown property doesn't change the fact that a dagger is a melee weapon. Throwing a dart, for example, would benefit from the -5/+10, because it's a ranged weapon. The thrown property isn't what's important here - what's important is whether the weapon is a ranged weapon or not.

If you prefer to hear it from the designers, Jeremy Crafowrd agrees that the first two benefits of Sharpshooter work with daggers, but not the 3rd. He also stated that a dagger is a melee weapon, even when you throw it, as well as including it in the official Sage Advice Compendium:

Does the Archery fighting style work with a melee weapon that you throw? No, the Archery feature benefits ranged weapons. A melee weapon, such as a dagger or handaxe, is still a melee weapon when you make a ranged attack with it.

Actually, throwable weapons are dealt with using their own tag : Thrown.

Thrown: Throw it at someone to hurt them. If you volley with this weapon, you can’t choose to mark off ammo on a 7–9; once you throw it, it’s gone until you can recover it.

(from the Equipment chapter, under Weapon Tags)

So, technically, unless the weapon has the Thrown tag, it cannot be thrown; your GM may rule it has the tag if it simply makes sense (eg. a well-balanced knife) or add a cost to it ("Wanna throw your bastard sword? Hmmm sure, but if you miss the blade might break after hitting the stone wall - or even hurt one of your buddies. What do you do?"), in the spirit of "Offer an opportunity, with or without cost" move.

See @BlackVegetable's answer about a related class move.