All assuming that the foe doesn't have the aerospace forces to oppose you. In space, even lighter ASFs can beat a LAM, and once you're in the atmosphere, then just like all other aerospace units you're vulnerable to the whim of the lawn dart gods, so even conventional fighters can be a threat.
If you go to ground to avoid the aerospace, then that's a mission kill as they've prevented you from taking whatever action you'd intended, and at worst you could be pinned until ground forces are brought up to flush you out or destroy you.
The counter may be that your own aerospace and ground forces can in turn engage the foe in the appropriate environment, but those LAMs have to come from somewhere. For every one that you have, that's one less ASF or Mech, and let's not forget the superiority of ASFs and Mechs in direct combat in their own environments.
As a small unit raider, scout or other spec ops role, then yes, but as something to build a large scale force around, you're asking for bad news.
You're absolutely right... except that this isn't intended as a line unit, but as a supplementary unit. Think about how the soviets used tank destroyers. Or attack helicopters, for that matter. Undeniably vulnerable and suboptimal for most situation, but very useful in a specialist role, so every higher-level commander gets a small unit (say, a company for every regimental commander, or a battalion for every divisional commander). So I'm not building force around LAMs, I'm using LAMs to supplement and enhance my ASF and especially mech forces.
Let's look at each scenario:
Insertion: Normally, I send in some ASF's to clear a route to either land my transports or orbitally drop my Mechs. Instead, here I replace a small number of my fighters and mechs with LAMs. The LAMs arrive with the aerospace fighters, but mostly ignore the furball and punch towards the LZ. On the ground, they secure the location for the dropships to land; alternatively, facing organized resistance, they redeploy to an alternate LZ (something mechs can't do unless your "alternate" is within a few km of the primary). They're relieved by the main force. It's essentially a hedge against a drop site ambush, something that in BT history often produces big casualties even when the attacker has a force advantage.
Combat engagement: I have a large force fighting along a multikm line. I accept that I'll have slightly fewer Mechs, but suddenly, a lieutenant reports he's making progress on one map square. So I deploy a company of LAMs, all of which hit that square and reinforce it. Faced with a sudden rush of overwhelming force, the enemy there collapses and I can either penetrate or divide or roll him up, depending on the situation. A force commander with only Mechs and ASF can't concentrate his ground forces as quickly, and can't hold ground with air support alone. Higher overall force tallies don't matter if I can defeat him in detail.
Operational flexibility: I'm in an invasion scenario and am hitting several objectives at once, perhaps separated by hundreds of km. Again, I use a conventional assault but I keep my small LAM force together, balled up like a fist, and they hit my objectives one by one. A very fast Mech moves at 10/15. A slow LAM (bigger but similar in armament) in ASF mode is crossing multiple mapsheets every turn. Whose reinforcements arrive first?
It's worth noting here that while my LAM force is clearly inferior to the specialist units, they also can swing roles, so the difference in numbers isn't quite as big as initially appears. Say I have six ASFs and 12 mechs. Now I replace a lance of Mechs and a flight of ASF with LAMs. So now I have 4 ASFs, 8 Mechs, and 6 LAMs. In fighter duels before landing, I can deploy 10 airframes (most of them crappy, admittedly, but numbers
do count). Then on the ground I have 14 mechs. So the hit you take in numbers and capability vs specialist units is real (not all those LAMs will make it to the ground) but not quite as bad as it appears at first glance. And the toy example above is way more LAMs than I'd take in a line force of that size.
Finally, there's a
forced withdrawal. My forces are on the way off-world, with enemy units pressing them hoping to over-run the drop zone. With no LAMs, either my Mechs have to fight as they're loaded aboard (something that happens all the time in the fiction) or my dropships take a shellacking from enemy ground forces as they try to lift off. Or both. I could try to hold a perimeter, but then I leave Mechs stranded to die after lift off. With LAMs, I harass the enemy pursuers in airmech mode, then hold a perimeter in mech mode while the last Mechs board their droppers. Then after the droppers lift off, my LAMs can transform and accompany them into orbit. Somewhat doable with normal fighters, comparatively easy with LAMs.
I'm not disagreeing with you that LAMs are extremely limited. Just that their strategic mobility makes them very useful in a wide variety of roles, so long as you don't try to use them as a major arm of service.