They'd have to be very weak or very end intensive, but I don't see that as being a huge problem for someone who, say, wants their scrapper to have a pistol for thematic reasons.
The only place this might bump into trouble is for people who already have weapon sets--as far as I know, you can only have one custom weapon, so they'd all have to be a "standard" weapon.
I could totally see a set like:
Snap Shot: Ranged Damage, Minor. Long-ish recharge, single target. (pulls out the standard desert eagle model)
Burst: Ranged DoT, moderate damage. Long-ish recharge and high end cost. Single target. (Uses the standard M16 model)
Micromissile Launcher: Enemy Targeted AoE, Minor damage. Fast recharge, but very high endurance cost (12-ish end per missile).
Flashbang Grenade: PPD Flashbang, hand-thrown. Very high endurance cost.
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The only place this might bump into trouble is for people who already have weapon sets--as far as I know, you can only have one custom weapon, so they'd all have to be a "standard" weapon.
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No, you can have more than one. Example: Create a Robotics Mastermind and choose Trick Arrows as your secondary. You get to choose both a Laser Rifle for your Robot set and a Bow for your Trick Arrow set.
The problem with a set like this is that it would conflict with other weapon sets and cause a lot of redraw. In addition, with the possibility of tank magery, the power effects would have to be lower damage or more endurance intensive than you might believe, unless of course this was suggested as an Ancillary Pool instead of a Power Pool.
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The only place this might bump into trouble is for people who already have weapon sets--as far as I know, you can only have one custom weapon, so they'd all have to be a "standard" weapon.
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You can have more than one. My archery blaster has munitions mastery and I can customize both my weapons.
~ Infinity Heroes ~
Dark Voltage - 50 NRG/NRG/EM Blaster
Shure Shot - 50 Arch/NRG/MM Blaster
Silent Shadow Blade - 50 Katana/SR/BM Scrapper
Uphir - 50 Fire/Fire/Fire Blaster
Yeah... Redraw...
Of course, you still have to Redraw with Kick, which doesn't even USE the arms. Lots of things cause Redraw. Frankly, I'm used to it.
I mean, Hell, the Shield set causes redraw with its Mez Resistance and the Shield Charge, and that set practically SCREAMS "Use weapons with me! It's thematic!"
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Flashbang Grenade: PPD Flashbang, hand-thrown. Very high endurance cost.
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Considering the PPD version of this power and what it does (you have to pray to be able to hit the enemies, and then hope your god looks down on you favorably), this endurance cost makes sense 
It would need a long recharge, too.
But it would be WORTH it!
My Stories
Look at that. A full-grown woman pulling off pigtails. Her crazy is off the charts.
I like this idea lot.My blaster could use these powers in the heat of combat.
Oddly enough, I know what you mean, Samson.
I had something happen to me in-game and I was playing my Peacebringer.
The PUG team I was on (and no, not a Horror Story PUG team, it was quite capable) wound up having to deal with a Cyst. Since I was the PB, I decided I should go deal with it.
Insp Drop and close-in later, I'm wailing away at the crystal, just chiseling its health. The Unbound Nicti aren't damaging me (couple Tier 2 Oranges in that Insp Drop), but they've got me slowed right down to a crawl. The Inspirations are about to wear out and I'm out of attacks.
So, I pop open my powers list and see if I've got Brawl or something to hit it...
There it was in Temporary Powers: Shotgun!
I slapped it in my tray and clicked. My PB drew her shotgun, pressed it against the side of the Cyst and squeezed the trigger.
BOOM!
The Cyst exploded and the Nicti went flying, tumbling to the other side of the Veil.
Single greatest moment I've ever done personally in this game, and I'm scat-scared I'll lose the shotgun on that character and never get it back, so I'm never using it!
Now, the idea is that the Shotgun will NEVER go away 
I want a power pool that would give me ready access to stuff like this.
Or make them into regular Invention Recipes... Whichever's easier
My Stories
Look at that. A full-grown woman pulling off pigtails. Her crazy is off the charts.
There's the Fighting Pool, which gives some melee attacks and defensive capabilities (as if a character has taken basic fighting training).
What if we had an "Arsenal Pool," one that gives extra "blasts" to characters. Probably largely ignored by Blasters and the like, but it would be nifty to get a Pistol power or an Assault Rifle. Later powers could be things like rockets or grenades and culminating in those nasty flashbangs the PPD Ghosts like to hit Villains with or perhaps get stable versions (i.e. no finite number of uses or time limits) of those Safeguard/Mayhem Side Mission Temporary Powers like the Shotgun, IR Goggles or Plasmatic Taser...
Okay, maybe not the Taser (it is just Energy Torrent with a different name, after all), but the rest would be nice to see more regularly.
My Stories
Look at that. A full-grown woman pulling off pigtails. Her crazy is off the charts.