Second of all, is there a reason that this works only against Vasari and not the other races? IRC they have constructor frigates too, and their constructors also rebuild 10x slower against the same strategy.....
That's a reasonable question. The answer comes from a combination of things, but mostly the poor performance of the vasari repair platform in combat. It actually repairs a fair bit of hp per AM usage, but at a slow pace. On a structure with an armor of 4 (extractor), the Vasari repair platform puts up an effective 15 * 1.2 = 18 hp per second. That's basically an extra 4 (un-upgraded) LFs worth of dps (which do only 50% vs. structures), so that level of repair quickly becomes negligible in the game, after just one fleet supply research. Once you get to a flock of 40 Disciples for example, the +10% lasers research (still one lab) is basically a counter for all the Vasari repair platforms ever built when they're repairing resource extractors. So in a typical LF spamming game, the research cost of the Vasari repair platform, plus a single instance thereof equals to the cost of its (research) counter. And the Vasari are probably going to need/build more than one repair platform.
The poor efficiency of the vasari fleet (per fleet supply unit) means that it's hard for them to defend (or attack successfully) with their fleet, so the Vasari player will rush for Orky. But the main problem with the Orky is it cant fight a fleet that doesn't want to fight it. In practical tests, a Progentitor + 50 Disciples can wipe out 2 constructors and 3 resource extractors (while they're being repaired) even if an Orky is wailing on them. And what's really glaring is that the Disciples can do that while taking no losses during this raid thanks to 2-3 casts of SR from the Prog. After which the Advent can move on to another planet (minus a constructor-rebuild-delay element.) And if the Orky doesn't have at least two hull upgrades, that is 9K hull, it is actually going to be the victim of those 50 Disciples+Prog, which can then shoot undisturbed at the resource extractors [and everything else in the grav well] after blowing up Orky. And that's not a cheap Orky costing about half the Disciples' fleet cost just to keep itself alive and relevant [about 6.5K in credits vs. 12.5 K in credits, ignoring the metal & crystal]. If the Vasari need to put an Orky like that at more than two planets, they're already spending more on defense than what the Advent is spending on offense... And while a beefy Orky keeps control of the actual planet for the Vasari, it can't really save the resource extractors at the planet, which are going to be out of action most of the time...
So what's different for other races in defending vs. raids on resource extractors? Repair platform efficiency for one. While the TEC one starts at 20 hp/sec it can be upgraded (and will be so because that is a prerequisite for other goodies, like Hoshikos) to 30 or even 40 hp/s. The Advent one also starts at 30 (but has no upgrades), but the Advent have shield bestowal available on their hangars with 3 mil labs, which more than doubles the life of structures with the added shield mitigation; the shield points themselves actually contribute less than the mitigation does. And the hangar's strike craft are also very good at catching and killing small constructor-rebuild-delaying forces. So the Advent hangar+repair platforms is basically a show stopper for extractor raiding, making those structures last much longer. TEC can basically stack Hoshikos (L3 mil lab) with their repair platform to achieve a comparable, but lesser durability effect on structures (50-60 hp repaired per second) and get +3 armor research (0.75 * 4) with the same 3 labs, resulting in a whopping 81 effective hp repaired per second on extractors (1.35 * 60). That's some 15-20 LFs equivalent firepower vs structures. Sure a bigger fleet starts wasting the extractors even through that, but that's plenty of nixed firepower, so the defender is going to be shooting at the attackers' ships for much longer with his own fleet, and the cost of the damage exchange is not looking favorable for the attacker; LFs vs. LFs do 100% damage, and even with the shield mitigation more or less doubling hp on ships, you can expect the defense to claim at least one if not two enemy LFs per extractor lost (even if the attacker brings its own Hoshikos) so the economic loss exchange starts to look unfavorable for the attacker. (Even more so for TEC as defender, because Modular Architecture makes extrator replacing cost 60% of their original value, i.e. 150 vs. 250. Even one corvette lost by the attacker basically makes up for that.)
Besides repair efficiency difference, when fleet A wants to run away after blowing up some extractor and it is pursued by an equally sized fleet B (instead of an Orky), the fleet running away will get shot at because fleets have similar speeds. Not getting into the fabled flak spam debate (which can shoot in all directions), the typical LF spam fleet can't shoot while it is running away, while a pursuant LF fleet can and will catch up at least at the jump out points, inflicting some extra retaliatory damage, on top of what was exchanged while the attacker was shooting the extractors. Although corvettes are less affected by this inability to shoot while running due to their all around guns like the flak, they are worse vs. structures relative to LFs (only 35% anti-structure efficiency vs. 50%) but they make up in numbers per fleet supply for that. Given their complex maneuvering, I'm hesitant to venture numbers of losses and actual attack efficiency of corvettes raid vs. structures followed by corvette after corvette chases. (Somebody should probably test that and perhaps post a recording.) My guess is that after receiving a corvette raid, the counter would be some carriers and/or TEC hangars with fighters and flak (on the hangar) but also flak ships which together would counter another corvette raid with a terrible loss exchange ratio for the attacker.