soft flux can cause overloads
Only at the overwhelming levels of a HIL / Tachyon Lance, at least in Vanilla, and there, rarely. The AI's shield-up behavior doesn't run every frame, apparently, or the Soft Flux damage is applied after it decides.
Other than those two weapons, I've hardly ever seen a Soft Flux Overload happen, tbh, even against weak ships (I think somebody brought that up last time we had this discussion, and I had to re-create it, because it just won't happen with Tac Lasers and Gravitons, for example); instead the AI drops shields for a few frames, then raises, while I frantically sweep the beam over the parts to either side hoping to do some real damage, lol.
Tactical Lasers and Gravitons can cause overloads in small ships. I've done it many times to Lashers when flying a Wolf with a beam armament. It's just a lot harder than it is with weapons that create hard flux, and usually it requires that the Lasher is already about to die and so cannot really afford to drop its shields while your beams are hitting it, or is afraid of an inbound missile, or something like that.
Also, I'd dispute that the HIL causes 'overwhelming' levels of soft flux. If it remains true that kinetic damage doubles the effective DPS against shields, a HIL is only 25% better against shields than a Graviton Beam is, and I'm much more likely to be able to carry a pair of Graviton Beams than I am to be able to fit a single HIL. Plus, the Graviton Beam is by far more flux efficient on my end. I can agree with the Tachyon Lance giving relatively overwhelming levels of soft flux (by comparison to other beams), but that's because it hits the target with a lot of soft flux all at once, rather than taking the more normal approach used by beams, which results in a steady trickle of soft flux generation.
What is the difference, in terms of Supply / Fuel efficiency, between an all-Frigate swarm at Burn 12, say, and a Destroyer fleet at burn 7? Does the increased durability / DPS of Destroyers make up for that cost, long-term?
It depends on which frigates and which destroyers you're using, but in terms of fuel consumed per lightyear per logistics point, the only purpose-built combat destroyer which is noticeably worse than most combat frigates is the Enforcer, which requires 0.652 units of fuel per logistics point to cross one lightyear at the standard skeleton crew level (even so, the Enforcer is still a more fuel-efficient choice per point of logistics than the Hound or the noncombat frigates). Hammerheads and Sunders are down at four ninths of a unit of fuel per logistics point to cross a single lightyear at standard skeleton crew levels, which beats every frigate except for the Hyperion, Omen, and Tempest, while the Medusa is down at 0.373 fuel per logistics point to cross one lightyear, which beats every frigate other than the Hyperion. Most frigates require less crew per logistics point than most destroyers do, which makes their supply consumption for equivalently large fleets somewhat smaller, but the Lasher requires more crew per logistics point than any destroyer, and the Shepherd requires as many crew per logistics point as the Enforcer, the most expensive of the combat destroyers (the Tarsus is equally crew-intensive per logistics unit, but it's not a combatant). The Medusa, meanwhile, requires less crew per logistics point than the Wolf, Hound, Lasher, Brawler, Cerberus, Monitor, and Shepherd. If you're looking at freighter efficiencies rather than combatant efficiencies, the destroyers win outright in fuel efficiency when you factor in cargo capacity, and probably also in supply use efficiency. All of this is assuming you're keeping the fleet at the standard skeleton crew levels.
I'm not really sure what point you're trying to make, but if it's that destroyer groups are less fuel-efficient than equivalent logistics values of frigates, that's mostly not the case. If it's that destroyers are less supply-efficient than equivalent logistics values of frigates, that's generally true, but even if you're looking at roughly doubling the supply consumption, it's still roughly 0.1 supply per day per point of logistics of destroyers versus roughly 0.06 supplies per day per point of logistics of frigates, which isn't a very big deal, even though a burn-12 fleet is roughly 45% faster than a burn-7 fleet (assuming that the lightyears per day conversion for hyperspace speed also holds in realspace). Fuel thus far has been by far the greatest single expense that I've had to be concerned with outside of combat recovery as a midsize fleet can easily use hundreds of it going from one system to the next, and there are clear and often significant fuel savings available for consolidating frigates into equivalent logistics worth of destroyers, especially if the purpose of both ships is cargo hauling.
If you're wanting to build a Burn 8 fleet, are there any Destroyers you want or must not have?
If you want Burn 10, to catch small Pirate fleets and push Pirate bases into Unstable, are there any Destroyers you can have at all?
What skills do we have, and do we have the theoretical infinite supply of Ox Tugs and the logistical capacity to use them, the money to afford them, the fuel and supplies to use them? Because if we have as many Ox Tugs as we want, any destroyer other than the Construction Rig can be brought to Burn-8 with Nav-2 and Augmented Engines (assuming you have or can find the ordnance points for them), and you can drop the tug at Nav-6 or the Augmented Engines at Nav-10 (but you cannot drop both the tug and the Augmented Engines). Medusas can be Burn-8 at Nav-2 even without an Ox Tug if you can put Augmented Engines on them. If you have enough Ox Tugs, you can make any arbitrarily large fleet of destroyers, Herons, or Falcons attain Burn-10 with Nav-10 under the assumption that you a. don't use the construction rig and b. have the ability to install Augmented Engines on each of your ships; Medusas can hit Nav-10 with an Ox Tug and Augmented Engines starting at Nav-6, and can drop the tug at Nav-10 (or reach Burn-11).
So yes, it's possible to reach Burn-10 with most destroyers, as long as you have enough skills and are willing to sacrifice enough ordnance points to pay for Augmented Engines and are willing to spend the resources required to have an Ox Tug per destroyer.