I assume this default limit of 2^24 is set by some purpose in BOLT #2. But what's the meaning of that? Or is there any test/experiment to support this number?
The goal was to limit the amount any individual adopter would lose due to bugs in the software. As explained by LN developer Rusty Russell in #bitcoin-lightning FAQ: Why the 0.042 bitcoin limit?:
I guarantee that early releases of lightning clients will have bugs and people will lose money because of them. […] I sleep better at night knowing that, if you lose money because of my bug, I can buy you a beer/coffee in exchange for your story and we’re about even. (emphasis in original)
This answer was sourced entirely from Bitcoin Optech: Large Channels where you can find even more resources on this topic.