It is a matter of preference, both are acceptable. In written form though I prefer your version:
But 15‐year‐olds, on average, probably take more risks than adults.
I think extra words creep in more often in spoken English when people are thinking on the fly and speaking extemporaneously because they are thinking more about making each part of the sentence make sense rather than visualising it as a whole as you do when writing.
Perhaps if you'd said:
On average, adults don't take as many risks as 15‐year‐olds do.
This seems more natural, because your "do" counters the "don't". But as it stands you are speaking about "taking" risks. You could write...
But 15‐year‐olds, on average, probably take more risks than adults take.
... but this seems even more bloated to me, and I'd bet that more people would agree the extra word is unnecessary in this sentence than in your original example. When you think about it though, there is very little difference. So I agree with you, lose the "do".