Agreed. Double heatsinks are the single greatest advance from the olden days to the modern era. More than XLs, more than any single weapon or any system of weapons, more than any gizmo or widget. No other tech has become practicly obligatory on every single mech, so much so that even if you don't need DHS, you still get a lot of flak if you don't use them (ie, Thunder Hawk).
A key problem would be refitting mechs. It would be best to use the most energy heavy load outs possible, since that would make the most of the DHS, and tweak mechs to run hotter (or take mechs like the Stalker and just bank the extra sink weight for armor or more guns). But, a nation like the Magistracy can't just quickly tune up all its mechs, or even a large number of them. It would take a very long wile for the tech to filter down.
That said, even at best, if you could not just refit all your mechs with DHS but also a complementery suite of energy weapons to take maxium advantage of them, you still wouldn't be more than twice as well off mech for mech, so a nation like the Magistracy still couldn't hope to take on a Successor State like the FWL. They could make a hell of a lot of trouble, and if they didn't get too greedy they could likely come out with some gains given the FWL's preoccupation with the other Great Houses. Gains in logistics would help a lot, too, given that you'd have very energy heavy mechs (in an ideal world) and you could have twice as much combat power per drop ship and per jumpship. But, the FWL still has so many more jump and drop ships than the Magistracy that it could still mount a counter attack twice or thrice as large if it needed to.
But, when you look a mechs like the Awesome 9Q, the Bounty Hunter's 3015 Marauder, or even some of the better 3050 upgrades like the Archer, you get a sense of what you can do with just that tech and no others.