The problem is when you give unsolicited advice, you feel like you're doing someone a favour.

You might very well, but they're not in debt to you. You might be giving terrible advice or the best advice, but based only on the limited information the person gave you.

Also, person giving advice can get a valuable feedback on their approach to problems.

I think the only problem is if someone is repeatedly giving the same advice over, which was discounted. But then the problem is that they don't learn and can't change their mind, rather than that they give advice.

Also, I recognise the fact that if someone is in extreme distress, they need emotional support, not somebody's problem solving.

Advise me. Or not.