In general if your tractor is standing still and you exert force on something, you won't break the tractor. Anything you have to take a run up at (swinging backhoe into it, driving FEL into it), or that you rock backwards and forwards, you have potential to be creating damage. And if you drive your machine to it's limits a lot, then you're working it harder than if you had a larger machine with larger limits. That's not just about the HP, it's about the beefiness of the machine itself - the L has I believe a stouter FEL and bigger axles and casings etc.
For mowing, back blading etc, those are all fine if done in a normal way. Digging with the backhoe pretty much the same given they're the same backhoe unit, again be careful on rocking back and forth or taking a run up.
When you get into ripping out trees or pushing them over, that's the kind of thing that breaks tractors. They're not really made for it. OK occasionally, but if that's a regular task, then get a backhoe or a bulldozer.
Most of it comes down to common sense.
I totally agree with you that any tractor you've mentioned, including a BX, will be enormously better than a shovel or a compact sedan. The question is whether an L would be better than an LX (aka large B). And I think the answer is yes in some circumstances, and the LX would be better in some other circumstances. If you want a cab, the answer is easy. No cab on an L, so get an LX. They are relatively similar machines in capability, the L is just built stronger. The L has a lot of supporters on here, as you're hearing, but each machine has its place. If you want a mid mower, a front snowblower, or a cab, then it's an LX (or a B2601). If you don't like digital dash, then it's B2601 or L. If you want more heft and more strongly built, it's an L.
Picking up a comment from earlier on digital dash - I agree with you I don't like them. But it wouldn't stop me buying the machine, it'll work fine for what it needs to, and I wouldn't go down to the B2601 just for that. I also wouldn't go to an L just for that - if it means you don't get a cab.
On the cab - strictly speaking your child isn't safe in the cab either. But I agree with you, I'd totally do that, and feel a hell of a lot safer in the cab than without.