Please read the instructions on the application of the LotG, it's in the same document - you're all giving careless a meaning that is not encapsulated by the instructions on how to apply the actual rule.
I've read those ElGrap. I think you have made it clear that you are relying on an interpretation that careless only applies in the context of making a challenge. And so you seem to be suggesting that running along behind a player and accidentally tripping them is not a challenge - so can't be regarded as careless and a foul. I think that's too much of a stretch.
I'm not meaning to be pedantic, I've discussed this sort of thing with referees and assessors and find this sort of thing interesting. I think partly because I came to the game late, through my kids, and had done a fair bit of refereeing in other sports so was fairly comfortable to offer to referee. But I had to learn all the rules from scratch and had to ask a lot of questions regarding interpretation, as well as read the rules carefully. And luckily I had a close mate who is a senior referee and two associates at my kids club who were also senior referees to chew the fat with.
So I may not be right, but this is how I would understand things.
Challenge is used in the interpretation and guidelines (amongst only a few other places) when discussing the offence of charging an opponent. In that case the wording is challenge "for space" So it is clear, I believe, that a challenge is not just a tackle for the ball. In the case of a charge, you may not play directly for the ball but you do contact the player, and it is regarded as a challenge, and a foul. The key point there is that you don't have to be challenging for the ball to foul, challenging for space counts too.
In the case of a trip I see the laws applying in the same way. You aren't (necessarily) making a play at the ball but you are making contact with the player in a way that disrupts their play illegally and challenges their space. So both a trip and a charge are challenges and fouls.
If you argue this is accidental rather than careless (or reckless or using excessive force), then I think you still have a problem. Referees can't read minds, so an elbow to the head, or a trip are both going to get whistled. At best you are going to be regarded as careless. Playing for a header you are expected to keep your elbows reasonably out of the way so you don't smack someone in the head. Running behind someone in possession you are expected to keep your feet reasonably out of the way so you don't trip them.
I'd also suggest this is not just the way I see it. Over and over, a trip from behind that drops a player in possession of the ball is called as a foul, even when this is just from a run crossing behind the player in possession. I can't see how you could interpret it otherwise. The player not in possession has a responsibility to not make careless contact. If s/he does make contact it almost has to be regarded as careless.
I might be missing something, but that's how I'd see it, same as O'Leary.
Apologies to those just enjoying the win.