Hi, there. I'm happy to help with this.

First of all, for the whole "clause between the commas" changes vs. doesn't change the meaning, I suggest you learn a little about the grammatical background --- restrictive clauses and, related to that, vital noun modifiers. I have attached two pdfs of blogs on these very topics that I just wrote last week --- these will appear on the Magoosh blog in the next week or so, but here are advanced copies.

Those blogs describe the basic sentence of the form

blah blah blah A, modifier of A, blah blah blah.

Instead, your sentence is of the form

blah blah blah A, modifier of A, modifier of something in the first modifier.

More than 300 rivers drain in Siberia's Lake Baikal, which holds 20 percent of the world's fresh water, more than all of the North American Great Lakes combined.

More than 300 rivers drain in Siberia's Lake Baikal = Independent clause

which holds 20 percent of the world's fresh water = relative clause, non-restrictive, modifies "Lake Baikal"

more than all of the North American Great Lakes combined = appositive clause, modifies "20 percent"

That's a completely different scenario. When you remove the middle modifier, of course the whole sentence is going to be discombobulated, because the second modifier refers to something in the first modifier, and if the first modifier is gone, the second modifier is modifying something that isn't there!

BTW, notice: the middle clause correctly has commas around it because it is a non-restrictive clause.

You have to be careful --- are you looking at

independent clause --- modifier --- more independent clause

or is it

independent clause --- modifier #1 --- modifier #2.

In those two cases, there are very different considerations at play.

Does all this make sense? For free, here's also a lesson video on related SC stuff:
https://gmat.magoosh.com/lessons/615-modifiers-i

I hope all that is helpful. Please let me know if you have any further questions.

BTW, thanks for the cool facts about Lake Baikal --- I had never heard of it before, but that's really cool!

Mike