Yeah, that's one of the points we've made. Beams work, but only when their Soft Flux > Dissipation Rate. A lone Frigate with Beams vs. a Cruiser with Hard Shields and maxed Flux dissipation, for example, does zero real damage; they're merely lowering the amount of time that the Cruiser can use its full DPS.
In the case of a souped-up Paragon, which is a bit of a ridiculous example, since ideal Paragon builds are usually constructed around using Fortress Shield (especially with hero buffs) you can, in fact, make Beams work.
But they only work because the Paragon can mount Beam broadsides that have Soft Flux damage higher than their opponents' Dissipation rates (at least, against Pirates / Hegemony, and note that Forlorn Hope features a lot of Frigates and Fighters that have no shield protection at all). The Odyssey can (very barely) make this work, too, sometimes, against smaller opponents.
An Odyssey is meat against an Onslaught that's equipped with Hard Shields, Stabilized Shields and reasonable Flux dissipation, though; it's Ballistic weapons do Hard Flux damage, the Odyssey does not, and the Odyssey cannot kite vs. Burn Drive. It only really works out with the Paragon, barely, and only because the Paragon is, well, the Paragon- the best tank in the entire game.
Saying that this means Beams "work" is not a very good argument- there are dozens of Paragon configurations that work, and several that (imo) work better, because they have better Flux / DPS tradeoffs, do Hard Flux damage in alpha strikes and are harder to kill.
So we're left with the arguments about the relative strengths of Beams:
1. If you have range buffs for them, their perfect accuracy means you can kite at ranges where Ballistics can't hit you. That, and none of the stock configs in Vanilla have Targeting Core yet, so you can literally out-range everything in your weight class with beams, Core and Advanced Optics.
But kiting literally doesn't matter if you cannot raise the enemy's Soft Flux if they decline to use weaponry. It matters to some extent in fleet engagements, but only if you have multiple ships with multiple weapons taking on a lesser number of enemies. Even then it's surprisingly marginal, because few of any given ship's Beams can bear on the target.
In most cases, they're a waste of your own Soft Flux; if you're also taking any Hard Flux damage along the way (say, the occasional rocket hitting your shields), it's getting more and more expensive to keep kiting, and the second you stop, the enemy regains any damage done- without venting... whereas you've taken some Hard Flux damage, have a lower threshold for Soft Flux, higher constant Soft Flux costs for firing your Beams, and must Vent to recover. I don't know how that's balanced, but it looks broken to me.
With smaller ships, this is a worthless build (which is one of the reasons why I got grumpy about this in the first place- it's a sci-fi game where my little ships can't use lasers).
If, on the other hand, they did Hard Flux, the ability to kite via Advanced Optics is a big problem for balance. I addressed that issue in my mod by making all Ballistics out-range all Beams in their size class, with a few out-classed via Advanced Optics but not all of them. That (and balance changes elsewhere) restored balance; ballistics have range, but tend to waste ammo at range due to shot speeds and general inaccuracy, Beams have accuracy but have to get closer and take hits. Ballistics tend to do Kinetic, so their hits are doing more real damage to Shields and therefore impact both enemy potential firepower and time-to-vent / time-to-overload; Beams with Hard Flux get parity, but they eat more Flux (that's a separate argument- I made Ballistics do zero, to make up for limited ammo, shot-speed / accuracy issues and their other flaws when ranges go higher than the really short defaults in Vanilla- if range bands stay how they are now, Ballistics probably don't need any buffs other than making sure they out-range Beams in their size class).
2. They're really great vs. fast-movers, because the turret AI for Beam weapons is almost perfect and a lot of the small ones have higher turret speeds than anything else. So you waste very little Flux on misses. And they don't have ammo issues.
That's great, it's a core strength, but it's a strength that can be addressed via balance; if they're just OP given that they deal Hard Flux, fine, cut their DPS a bit or raise their Flux costs or both. Then they're good vs. fast-movers, but are more marginal vs. bigger targets. They're already nerfed that way to some extent because they're ENERGY-type damage, but further nerfs aren't a big deal, if they're actually necessary.
But there's a wrinkle to that that a lot of players don't appreciate. Beams do waste little Flux, yes, but their theoretical DPS is rarely their true DPS- just like Ballistics. Ballistics get more and more efficient as we close on a target, Beams have a flat profile. So a Beam that looks great at 600 SU is looking a lot less cool at 300 SU (which is one of the reasons why the Vulcan is surprisingly useful, even with its wimpy Frag damage).
I think that one of the tradeoffs there is that Beams probably need to be less Flux-efficient than Blaster-type weapons. That would make Blasters an intermediate type between Ballistics and Beams- some of the strengths and weaknesses of both. That's basically how I have things in my mod atm (although generally, I also give them greater range, and made them snipers, instead of being very situational point-blank strike weapons, but that's another argument).