... these are the same "kings of the battlefield" which can trip, fall, and explode without ever taking enemy fire due to spectacularly bad dice?
Well, yes:
That's an Israeli tank flipped over during a training accident. It's easy to find more on the subject if you're keen - any vehicle is only as good as its driver/pilot/operator. And yes, you do have to fail a piloting roll to "trip, fall, and explode".
See, I don't have a problem with infantry being "weak", I have a problem with them being literally too much trouble to figure out and having math which means having to work for a couple hours for something which isn't useful. (Not even against vehicles.) As it is, they're not a hazard to anyone, not even in the same feel as a minefield, because if it's not battle armor it's too much trouble to make them in large enough numbers to actually achieve that feel. And battle armors wind up being a legitimate speed-bump at worst, and game-breaking at best. While still potentially taking a lot of time to figure out how they work on a battlefield.
I don't know what we do/did differently, but I never found them to be much of a hassle; just stipulate you have one platoon of laser infantry, one of SRM infantry, and a couple of bastards with flamers hiding in yonder basement and you're good to go. Sure, it's a bit more book-keeping due to there being more units on the field, but if you can do 16v16 in four hours, you should be able to do 4v4 + infantry just as easily.
Now, I'd have not thought of all this if I hadn't been discussing CBT over the last couple weeks and the topic having turned to "how many rules which are meant to simulate battle really are useful and not just adding more time?" Which eventually turned into noticing about 50% of the Total Warfare book content isn't going to see use, and about 70% of the special equipment listed turns into "why?" more than "how does this work?".
If that works for you, more power to you. Most of the rules of the game are meant to be used if you feel like they're worth it. If not, just skip them - same as with any RPG rule-set or any other game with "advanced" or "optional" rules.
I mean, I actually
like spending time working out exactly how long it takes to repair battle damage for my own solo-play or in campaigns with like-minded crazies, but when I'm with friends and we're just playing a couple of quick matches I absolutely don't bother with that. The 'Mechs are just magically combat-ready for the next battle.
It's like those D&D stories where someone dies to a cat scratch.
Ah ha ha, you played right into my trap!
(credit: Murphy's Rules, by Steve Jackson Games)