If you took the original post to mean that weak evidence isn't common, I'd contend you took the wrong lesson. Encountering strong evidence can be a common occurrence while still being much less common than encountering weak evidence.

You are constantly bombarded by evidence all the time, so something can be true of only a tiny fraction of all evidence you encounter and still be something you experience many times per day.

Also, each observation is simultaneously evidence of many different things.  When someone asked if you were evil and you said "no", that was weak evidence against you being evil, but also fairly strong evidence that you speak English.  If I put my hand out the window and it gets wet, that's pretty strong evidence that it's raining outside my window, but also weaker evidence that it's raining on the other side of town.

I think you're right to point out that just because strong evidence is common in general doesn't necessarily mean that strong evidence about some specific question you are interested in will be common.  There are definitely questions for which it is hard to find strong evidence.

But I don't especially trust your generalization of when strong evidence should be expected, and I think some of your examples are confused.

In asking how hard it is to get evidence that you can beat the stock market, I think you are misleadingly combining the questions "how likely is it that you can beat the market?" and "in worlds where you can, how hard is it to get evidence of that?" in order to imply that the evidence is hard to get, when I think most of the intuition that you are unlikely to see such evidence is coming from the "it's unlikely to be true" side. (Also, it is actually not true that getting >50% of trades right means you will be profitable, because the size of the gains or losses matters.)

And asking someone "are you overconfident?" may not give you very much evidence about whether they are overconfident or not, but that's probably far from the best strategy for gathering evidence on that question.

One time, someone asked me if I was evil. I said "no". Afterward, they probably didn't believe I wasn't evil. I'm guessing they wouldn't have happily accepted a bet at 20:1 odds that I don't deliberately hurt people.

What would you expect a person who's evil to answer? I wouldn't expect them to answer "yes" but "no" is the most likely answer that I would expect an evil person to give. 

Saying "no" means that you refuse to give any evidence that you aren't evil when exposed to the question, which seems to me a tiny bit more likely for someone who doesn't really have that evidence. 

Theoretically, a trading method that gets over 50% of its trades right will be profitable. 

That's not true. Different trades have a different impact. A trading strategy that gets 90% of it's trades right but makes one trade that bankrupts the whole company is not a profitable strategy. 

Seeing an Onion headline say "X did Y" is teeny evidence that X didn't Y. 

I think that's doubtful. Most Onion headline are about events where there's a strong prior against the event happening. 

Sometimes a true statement still makes for a good ironic article. One of the greatest articles by the German equivalent of the Onion, Der Postillon, was an article about how politicians want to change processes around rescuing migrant ships because too much of them had migrants drown in a short time frame. Being very explicit about the game theoretic position where the Western politician are okay with a certain amount of ships drowning isn't something you would have read in normal news sources but which is both true and funny.

Putting a claim into ChatGPT and getting "correct" is little evidence that the claim is correct. 

Unless your claims are heavily preselected e.g. for being confusing ones where controversial wisdom is wrong, I think this specific example is inaccurate?  If I ask ChatGPT 'Is Sarajevo the capital of Albania?', I expect it to be right a large majority of the time.