Rule-wise, LAMs have always been either completely broken, or total crap. There is no in between. I didn't know anyone who wanted to play with them, because there really wasn't a way to balance them. While they were cool, they weren't really fun. Originally LAMs could carry bombs and used the old strafing rules. They weren't so hot against aerospace fighters, but if your opponent didn't have them? They were monsters.
TPTB tried to throw LAM-lovers a bone by bringing them back for the Jihad, but then pissed the same group off by saying "oh yeah, LAMs were never really very good". This went against basically all the previous background information, when they were seen as super valuable and wonderful, and rare but not actually lostech. I understand the real world reasons for it, but the explanation seemed forced. It is what it is.
In-universe, the way to use LAMs is with overwhelming concentration of force. An Overlord dropship carries 36 mechs and 6 aerospace fighters. Or it can carry 6 aerospace fighters and 36 kinda crappy aerospace fighters. And with that kind of force you can blast right through the air defenses that would normally be used against a Battalion. You can redeploy anywhere you need to, avoid the bulk of your opponent's forces, and pick them apart at your leisure.
A Phoenix Hawk LAM is going to get blasted to pieces by a Warhammer or a Marauder (unless you really abuse the Airmech rules). But 4 Phoenix Hawks at once against that Warhammer will chew it to bits. Unfortunately, we're back to square one, because that's not going to make for a fun game. LAMs really come into their own when you consider strategic movement and positioning of large units. That's just not Battletech though. Battleforce maybe, but not Battletech.
So what do the people of the Inner Sphere think of them? An amazing piece of technology, but one that's best in groups. They'll probably look to sell it to somebody who specializes in that sort of thing.