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"A customizable profile would be a better feature."
Agreed. Any stickied topic that isn't locked will be spammed and derailed. It wouldn't be a big deal if that happened, but it would defeat the purpose of why it originally was stickied in the first place.
...on second thought, maybe a stickied topic could make a fun experiment. Probably not, but it could.
Making an archive topic would work better, but we saw what happened when emilynghiem tried those (poorly). 
I was also concerned about spam. Nevertheless, whilst a customizable profile is a decent option as well it does not provide an access to all the data in once place. I don't see a reason we couldn't have both. Besides, it doesn't hurt to try.
"It is a good idea in theory, but I don't know how many people would actually bother to fill it out, at least in an honest way."
Here's the thread.
"The ability to search someone's past posts would be good."
You mean the search function right above chat? I love that thing. It's a little raw, but it does the job if you remember enough details.