In the Language Construction Kit 2, the author makes the assertion that sub-clauses, in particular center-embedded clauses, add complexity. That is obviously true, but he claims that you can make do without them (its in a section where he's talking about auxlangs and what features he thinks you should avoid).
But are there any languages that actually lack this? Thinking about it, it would be hard and rather clumsy to have to break up center-embedded clauses into separate sentences, but that may be just because I'm used to having such a convenience.
I do know that languages differ on how complex a sub-clause can be. English allows constructions that wouldn't be allowed in other languages, but there are still things that some languages allow that English doesn't.
I don't believe I've ever seen a serious auxlang (unless you count Toki Pona, but that was more intended to be an artlang) that didn't allow sub-clauses. I even found an auxlang called 'Kah' whose grammar is obviously based off of Chinese, but even that allows sub-clauses and even center-embedding (which is surprising given the lack of explicit marking on anything).