Note that a couple of completely new 'Mech designs were being fielded just before the discovery of the Helm core: the Wolfhound and Hatchetman being among them. The recovery was already and clearly happening by 3030, and then the Helm memory core boosted that recovery up several notches, but not in time for the 4th Succession War.
Unlike the 1st-2nd SW, the 3rd was not a war of annihilation, where planets were being depopulated and/or their industries reduced to rubble. The worlds behind the more-or-less stable borders had over a century to patch together everything that could be gotten working again, and even started building entirely new facilities, although at a lower level of technology than before. That newly built (or repaired) production capacity was used for a covert buildup, which was carefully hoarded by several of the Great Houses to provide a modest material surplus to launch the 4th SW. Even with that surplus, it required commandeering and redirecting a significant portion of the civilian Jumpships to conduct the invasion (at great cost to the civilian economy), so the territorial gains were still fairly modest by 1st and 2nd SW standards.
Basically, full-scale warfare on the scale of the 1-2 SW would only be possible with a massive buildup of space assets, which are still fairly rare in the later stages of the game's timeline before the sudden jump forward to cover the 32nd Century. Given the massive cargo capacity of most of the SL warships, it does appear that they were the primary jump transport for invasions, with the bulk of the forces being moved from them to the planet's surface by dropships or small craft. The dropships would have been used to secure the initial landing zone, then made repeated trips back and forth to the orbiting warships for the bulk of the invasion force and some initial supplies. More intensive supply runs would have followed, eventually using more conventional cargo Dropships to and from the already well-secured landing areas. Without those warships carrying large invading armies, the Successor realms are forced to fall back on the relatively tiny dropships as the primary military transports, and use civilian jumpships to get them to the system. That seriously restricts any grand invasion plans to mere raiding and the occasional change of hands of one or two planets in an "all out" attempt.
While I agree that something beyond a never-ending series of minor raids was needed to put some life into the overall timeline, doing so without the corresponding increase in the REAL bottleneck (interstellar transportation) seems misplaced or simply unrealistic. With transportation, you can have warfare with conventional vehicles, 'Mechs, and infantry on a grand scale. Without it, fielding a mere handful of 'Mechs against an entire planet's defenses can't reasonably be explained except as quick "smash and grab" raiding. The universe needs either a MASSIVE increase in the number of jumpships and a new set of dropships designed for the new realities of 31st Century warfare (NOT for the way the SL did it), or else the reintroduction of large warships as interstellar invasion transports.
As it stands, the entire universe concept has neither embraced the "Mad Max" style of scrounge-tech with limited resources, nor fully transformed that universe into one which has finally come to realize that they CAN'T fight warfare with SL strategies unless they have the SL tools to do so.
The Periphery has been the most interesting part of the setting for me, in part because the IS itself is so clearly and inherently dysfunctional, with that unresolved dichotomy between the original static setting and the far more actively rebuilding retcon throwing the proverbial wrench into everything. In the Periphery, that scrounge-tech style is still the norm, but with the rebuilding economic strength of the IS providing some occasional spare parts from outside the primary scope of the setting. That works for places like the Aurigan Reach, other than the sheer numbers of 'Mechs present in the video game for such an economic backwater area.
