I know I'm going to get flamed for this, and there will be a lot of people who think I'm an idiot for saying it (because "Don't take my crutch, bro!"), but I really think that it would finally help to achieve balance between the suits.

The old argument that shotguns are only effective on scouts has been proven false, again with the "new"ish trend of speed tanking an assault suit and throwing a shotgun on it because you can reach scout like speed with higher EHP than said speed tanked scout. With the cloak delay/slowed weapon swap, you don't get insta-ganked by cloaked shot gunners as much any more either.

Heavies can use all weapons, they are the largest suit in the game, Mediums can't use heavy weapons, they can however use light and side arm, Light frames should have 2 (two) side arm slots for their weapons instead of a light weapon and a side arm because they already receive the benefits from having a higher base speed, lower profile, higher precision, smaller hit box, and the ability to fit a cloak, or tank themselves to near medium frame EHP values.

Side arms have high alpha damage weapons still, Knives (Best used on the Min scout, with the worst over all Ewar capabilities). Bolt pistol (The highest damage and range per shot sidearm we have). The Breach/Scrambler pistol is a beast (419% damage for head shots!). The Ion pistol has a great clip size, good damage and dispersion once you level up sharp shooter, and has a charge shot that yes while it over heats in 1 shot, can drop most medium frames in that one shot. Flaylock is great for clearing objectives/equipment, and is basically a hand held small missile turret. Mag sec, yes it has a slight charge up time, but it has decent range, clip size, and damage (Can be run as a main weapon as well).
The only side arm that needs some love is the SMG (Why fit a PRO assault SMG when the STD assault CR does more damage, at a longer range, for a lower fitting cost, and less ISK?), and the breach, while it does do decent damage and has a large clip size, really only has an optimal of ~28m
It would be nice if every race had at least 2 side arm weapons to chose from (Gallente and Amarr only having one currently)

I can already hear it coming from all the scrubs who need this OP current setup to do well screaming "But then I'll get slaughtered by heavies and medium suits!" I need my scout with my SCR/ACR/BrAR/SG/Whatever to kill everyone else."

Let me be very clear on something. You are a scout, not a light assault, not a light heavy. A scout. Your role on the battlefield should be to orbit the squad you are running with (Even if you run solo mostly), follow the pack and only break away when you see a clear opportunity for a quick/easy kill/hack.

It gives every suit a clear and defined role on the battlefield, scouts are still the hard counter to a heavy camping a point. (You have a lower profile, can cloak, have better scans and speed, and also fit REs), and it stops the whole issue of a single brick tanked scout being able to rush head on against a medium or heavy framed suit without at least thinking of an alternative way to kill said target, or get past them for a flank.
Assaults and Logi suits still fill their role being the primary combat suits, heavies still get to be the waddling death machines that hold points from the masses or ride around in their murder taxies ganking groups and lone wolves, and scouts get a clear and defined role to fill being the infiltrating hackers, link layers/killers, assassins that they should be. Without everyone trying to run one type of suit to fill all rolls.

I'm not just some noob who is pissed off at scouts, I have all 4 (Min and Gal PRO, ADV Cal, and soon to be ADV Amarr. I'm working on getting PRO with them as well), 2 PRO Assaults (Min, and Amarr. Will be working on Cal and Gal once I finish skilling up the scouts), 2 PRO Sentinel (Min, and Amarr), Min Commando PRO, and Min logi PRO. As well as CR, SCR, MD, SG, LR, Swarm, HMG, NK, Mag sec, Bolt pistol, Flaylock. All maxed out aside from fitting optimization on a few of them. All my core skills aside from Active scanners, hand to hand, and cardiac regulation are maxed out as well.
I'm sitting on ~92 million SP, so yes, I've tested these fits and had this thought for a while, I'm not looking to give myself an advantage in any way shape or form.

I'm after some actual balance in this broken ass game.

Ever noticed that the scout problem almost immediately went away once the EWAR mechanics were overhauled? I'm seeing more and more assault suits being used for assaulting and less scouts being used for assaulting. From what I see, the scouts are no longer able to outclass the assaults. As the OP said, there are some assaults that can even run almost as fast a Minscout can. Hell, I have seen such assaults already.

Scouts should only have 1 light weapon slot and 1 equipment slot.

Oh yeah! I forgot about that. I've learned that I can only deploy 2 uplinks at once even on my proto scout suit because I only have enough room to fit one pair of R-9 Drop Uplinks after having to fit the cloak due to the recent EWAR changes. The cloak delay did have a major impact especially on the shotgun users. I'm no longer seeing shotgunners blapping people while their cloak is still diminishing. I don't know if strafing has been adjusted yet though to account for HP modules fitted.

I honestly have less of a problem with the light assault idea as the OP may have eluded to it.
The whole point was to get people talking about how to get the scouts Ewar back to a more usable state.
I still love running my Minja, my Gal/SG combo, Cal/ACR. Only thing on all my scouts that we've noticed is that the Ewar on the suits is very underwhelming over all.

Yes, I know that limiting scouts to sidearms would only mean that we would see more sidearm kills, and that it wouldn't really downplay the lethality of good scouts. I generally run my sidearm only min scout with mag sec and knives and do very well, but if it would get us our Ewar back, we would support it.

The Concentric Circles don't give any suits more HP and you can get under their passive scans with enough profile dampeners in the lows which is what the circles are trying to get you to do if you're in a scout suit.

I have plenty of beef with scouts who tried to tank up their suits thinking they only need the suit's innate profile dampening advantage. With concentric circles, only scouts who fitted enough dampening mods -- in my case it's one or two complex damps mixed with a kin cat on my minscout -- can get under those circle scans effectively which meaning they have to sacrifice a lot of tank to get that close. The cloak helps with hiding scouts from the dedicated scanner logies, but that's usually the extent of the cloak now. Since it reduces the passive scan range of the user once activated, you don't really see medium suits use it especially when the cloak gimps their CPU/PG availability.

The point here is that the scout can't outclass the assault anymore and the assault can't outclass the scout. This reinforces both roles as now both suits are no longer marginalizing each other.

However, I do have to admit that those range amplifiers may need to be looked into which I feel were overnerfed since 1.10. The reason the Caldari scouts are where they are now is because the range amps have been gimped which diminishes their roles. Not sure about the Amarr scout though.