What I don't like is that they're too much of a "fallback option" right now, when it would be cool (not that they should be to make the game better, just rule of cool) if you could, if you so desired, build a PC that focuses exclusively on chucking stuff. (Or we could say a [short] ranged fighter that doesn't have to switch weapons when [if] he gets to melee)
What I'm saying, I guess, is to make them competitive to ranged weapons, with the extra range from dedicated ranged weapons making them better to stay out of harm's way or to stay hidden (also, in a 1v1 vs an archer, the thrower is in for a world of hurt). They shouldn't be on par with "big" melee weapons, like greatsword, glaive, etc in melee, but the added damage in the rounds spent closing the distance (which, if you run around, may be quite a few) should even that out. Once you get close though, the difference becomes apparent, with the dedicated melee being clearly superior.
I'm going to think about this though, since it's a really good question; I'm hesitant to even post this since I haven't thought all the way through, but these are my surface thoughts on the matter.
OK, lets just say, 3 weapons do 1d8 damage (Longbow, longsword, spear). Now look at what they
can't do. The Bow is hampered by being useless in melee and requiring 2 hands, and the Longsword can't be used other than melee. Now what can't the spear do? well it can do what the bow does (attack from range), and it can do what the longsword does (Attack in melee). Therefore, it's demonstrably better because you don't need two weapons. Therefore, it makes sense to dial down the melee damage (because it's not dedicated melee), and dial down the range (not dedicated range), BUT it still keeps its main USP of attacking in both situations, which the others can't do. As I said, it's a feature, not a bug.
If you were to "Bring the damage" up in line with a ranged weapon, that balance is broken, because now you have a hard hitting ranged weapon you can use in melee. And as you pointed out, your additional options bring your damage output up to a big 2-handed weapon level, but now you can carry a shield at the same time. So why take a longsword?
IF, however, you want to be a cool dude chucking knives/chakrams/javellins about, then either reskin/reflavour/build a standard ranged weapon and take all the penalties associated with balancing it (crap in melee), let the long range sharpshooter feat apply to thrown weapons.
Hell, if you wanna go mental, get a barbarian class with Sharpshooter, Two-Weapon Fighting (draw two weapons), and let them dual wield javelins. Reckless attack at 120ft? Yes please. (RAW states 'melee weapon attack' - javelin is a melee weapon).
My point being, yes it may well be cool, but you'd be breaking the core balance between range, melee, and thrown weapons. And if you want the cool imagery of being a knife thrower, then just design a new weapon that works like a hand crossbow if you ain't going to melee much.