Personally, I'd love to see the weapons actually seem like they were testing something. Either a perk that doesn't normally land on that archetype (shotguns with explosive rounds, a full auto hand cannon, or maybe a sniper rifle with a Sureshot IS instead of a scope), or something even more extreme (a shotgun with vortex, "find more special ammo", and performance bonus, as well as full auto, for example, or a bullet hose auto rifle with minimal stability that uses skip rounds and has a massive clip... Stuff like that.

It would be really interesting to have prototypes with new gun features, but that would require adding new content to the game. So far, that's been more difficult than it should be for Bungie. That said, I'd really like it if the prototype weapons had interesting features that could make them very powerful, but since they are prototypes they should also have significant problems. Maybe a shotgun with firefly occasionally damages the player as much as their opponents? (Actually, that's the tradeoff ice breaker should have had. Infinite ammo, but sometimes the gun "misfires" and damages you instead or pehaps it overheats and if you don't watch your shots you'll take damage?) Perhaps a sidearm that hits targets behind your targe but is extremely unstable and has a tiny clip.

Personally, I'd love to see the weapons actually seem like they were testing something. Either a perk that doesn't normally land on that archetype (shotguns with explosive rounds, a full auto hand cannon, or maybe a sniper rifle with a Sureshot IS instead of a scope), or something even more extreme (a shotgun with vortex, "find more special ammo", and performance bonus, as well as full auto, for example, or a bullet hose auto rifle with minimal stability that uses skip rounds and has a massive clip... Stuff like that.

When I first heard about the concept, I thought it would all be stuff like this. And the fact that you have to kill specific enemies (usually majors) just makes it feel like a total chore.

I'm going to come off as a bit overly negative here, but I truly believe what I say. The simple answer to your question, IMO, is that Bungie didn't put much though into it. Like many of the peripheral systems in Destiny, the gunsmith is nothing more than yet another repetitive activity to keep us grinding yet another rep meter in the hopes of yet more RNG-based rewards.

I bet there was a small amount of conversation within Bungie at some point where a couple designers said "we don't want to make the Gunsmith weapons OP, right?" "no, just make them all crappy to be safe". They came up with a handful of test weapons (how many are there? 10? I don't actually know) and designed a small set of corresponding bounties, and threw it in the game. All of it is under-developed, makes very little sense in terms of how it fits into the fiction of the game world, and adds virtually nothing in terms of unique or rewarding gameplay experiences.

All that said, I think there is plenty of potential in there somewhere... the Gunsmith could certainly be worked into the game in interesting ways in the future. For example, what if the prototype weapons functioned like true prototypes: Awesome and creative new features, but they don't always work quite right. A rocket launcher with a DEVASTATING payload, but once in a while a projectile will fail to detonate. A new machine gun that has a super-fast reload, except that it jams every now and then.
How about new weapons that don't fit into the current archetypes? A flamethrower? A laser-gun? Grenade Launcher?

As Blackt1g3r already pointed out, these kinds of additions would require more substantial work from Bungie. It seems to me that Bungie has entered "The fans need content, lets get stuff out the door no matter how underwhelming it is!" mode. Personally, I'd much rather have longer waits between updates and get genuinely substantial stuff added to the game.

They just weren't tied to a reputation system that eventually gives you more shitty weapons.

I'm pretty sure Bungie wanted people to try different weapon styles. The whole Gunsmith thing was the reward system to encourage testing a variety of guns.

It was exactly this testing that led me to the HAKKE D series of weapons. Ultimately I found the Arminius-D to be my favorite gun. Co-incidentally it was so powerful they had to nerf it (not enough to make me switch though).

I continue to test the gunsmith's weapons. Bungie seems to make changes in the line up. I like being reminded why I do or don't like a weapon's characteristics.