However, I'm going to have to disagree with your assessment here: you can't treat the two playstyles' use of the map as equivalent. You say, "they can do the same thing," but they really can't. The two teams have access to the same terrain, but the things they want (and the way terrain affects that) are different. Sure, they can maneuver through all that low cover too, but they can't do that and be shooting you inside your cover at the same time. Even poptarts (which are more common than they used to be, but still fail to dominate the battlefield as in days of yore,) can't shoot at you from one valley to the next. Mobility is also a consideration; while you do see some big, slow brawlers (like my beloved Atlas,) many brawling builds rely on speed to close the gap - they may not be the swiftest chariots in the race (since they want armor and guns when they get there,) but they are notably faster as a demographic than your typical missile boat.
We can't postulate that one side has all the LRMs and snipers, while our side is just trying to brawl. That's not a reasonable force mix even in maps perceived as more short-range, much less Polar Highlands; it's more realistic to expect that both sides with have a mix of forces with long-range builds over-represented compared to other maps. So you're not going to be trudging through the snow under the cruel eyes of endless UAVs and high-explosive rain while the enemy is all optimized long-range builds with dedicated scouts on their side - in most matches. When you are, though, it feels like it. Trust me, I played an Atlas Brawler throughout the heyday of the Poptart Meta, I know the feeling:
But typically, it's not really the case.
It's also unrealistic to treat scouting as unopposed: if we don't have any Lights, it may be a rough day; but what about the times they don't have any lights? What about the many, many times that all you have is a laserchicken or ERLL Arctic Cheetah for your Light component? It's necessary to consider how an asymmetric force mix affects map balance, but for general balance discussions, a more even distribution of roles and tonnages should be assumed.
My advice in this thread (and the mini-guide I posted) is based on my own observations playing the map in the PuG environment. Maneuver warfare isn't a magic wand to wave at LRMs and make them go away, but it will produce victory more often than not with a typical force mix. Certainly, Polar is a tough place to face LRMs in certain circumstances - but it is those scenarios which are idealized. If you have a perfect storm of team composition and tactics, Polar Highlands is a hellish place for the disadvantaged side. Of course there is a problem with the depth of the cover available - but it doesn't break the map in most games. And, like AMS, no one who refuses to use a counter-tactic should expect complaints to be taken seriously.
(Also, remember that I didn't say, "just bring AMS and it's fine." I said "no one who refuses to use AMS gets to complain about LRMs," and parried an objection to that statement by pointing out that AMS really is worthwhile in the current tactical environment. Even so, your analysis of AMS effectiveness misunderstands an important point: you're not bringing AMS to shoot down all their missiles - you're bringing AMS to provide damage reduction from those missiles while you close on the LRMs.)