Legalization does not mean lack of any regulation. Alcohol and nicotine, which are legal, are regulated, as you point out. So are prescription (and even non-prescription) drugs. I am not opposed to forbidding sale of legal drugs to minors, though it's not perfectly clear cut (the age limit is particularly tricky to set, and often minors manage to get their hands on alcohol, nicotine, and other drugs anyway).
"Do you have withdrawal symptoms if you stop [skydiving]?"
Actually, I have read of people who did feel like their depression was alleviated through participation in extreme sports like skydiving,[1] and who feel depressed if they don't go again for extended periods of time. So I think a psychological addiction (much like addiction to food where similar effects are seen) can apply.
"Does it make you unable to function and think clearly for a while? Is your judgement affected enough that you'd harm yourself or someone else to participate in the sport again?"
Depression can affect your thought process, and can lead to harm of self or others, so yes, I think those are real risks of quitting for some people who get relief from depression through participation in extreme sports (or other perfectly legal activities which either help them to cope or alleviate their depression).
[1] - "Skydiving Cured My Depression" - https://news.ycombinator.com/item?id=16837748
Heavy addiction: you have X problems, you escape via addiction, now you have X+addiction problems, you stop, you still have X+addiction+withdrawal.
Hobby: you have X problems, you find something that helps you with depression, you have X-1 problems, you stop, you have X problems again.
Most people would not even seriously consider making extreme sports illegal, despite their danger and potential addictiveness, but it's those very same properties of some illegal drugs that are most frequently cited as the primary reasons for making them illegal.
If those are honestly the main reasons that so many drugs are illegal, then why not make extreme sports illegal as well, for those very same reasons?
They are regulated to an extent. You will get fined for selling to minors, for example. Same for smuggling cigarettes and alcohol. And for misleading advertisements and fake medical research. I don't think those fines go far enough.
> Skydiving and other extreme sports are often described as highly addictive and are obviously dangerous, yet no one is trying to prohibit them.
I'm not sure "highly addictive" works here. Do you have withdrawal symptoms if you stop? Does it make you unable to function and think clearly for a while? Is your judgement affected enough that you'd harm yourself or someone else to participate in the sport again? This is a "fun hobby" that will make you sad if you don't do it again, not addiction.