I do want to see those emails. Which is why I run my own mail server where I control what does and does not get rejected. BTW Google and Microsoft do reject or worse, silently drop tons of legitimate mail for such great reasons as the sending server having a bad actor living on the block some time in the past. Mail filtering is a really bad argument why you wouldn't want to see what is hidden from you by the incumbent providers.

Running my own crawler is unfortunately not as realistic.

You can't say that for anyone else. No one can say that for anyone else.

And, repeating, unsolicited communication is different from search results.

But in fact yes I do wish I could trust that my spam folder was actually complete. I find false positives in there all the time. But my point was that even if it's incomplete, you still have a spam folder that you can choose whether to look at or not. The fact that some stuff is filtered by other parties before reaching my client or server is irrelevant.