This is a common misunderstanding, and I don't want to sound like I'm blaming you for it, but it's based on a misconception of how the process works.
What interviewers are looking for is genuine introspection of the kind a high-quality hire would be expected to have. One answer I've given before, for example, is that I instinctively focus too deeply on technical requirements; I have to regularly prompt myself to answer "why does the customer care", or I get too deep into the details and end up with solutions that fail to serve their needs. The fact that I can recognize this weakness and take action to mitigate it is a positive signal.
What interviewers are looking to avoid is terrible answers that reveal underlying flaws or show you can't introspect at all. "I don't have any weaknesses", "I have trouble dealing with dumb people who give me bad ideas", "I get frustrated when people come to me with problems but don't explain what program I should write to solve them", etc.
Lame, humble-bragging answers are not the intent of the question and will not impress the interviewer, but probably won't prevent you from being hired if the interview otherwise went great. So maybe they're useful strategically if you're worried about giving a bad answer.
This 100%. An actual honest answer got me my first post-academia job. I had originally tried the "I'm introspective, so I actively work on any problems I find." When I could tell the interviewer was not impressed with that answer, I just fessed up. "I'm impatient." Not only was the honesty refreshing, but the interviewer shared the same problem. It was a nice bonding moment.
I don’t think “I focus too much on technical requirements” is a great weakness. That’s pretty much a standard pitfall most technical people would fit into. A greatest weakness is “I procrastinate a lot and wait til the last moment to get started on a project and often miss deadlines” or “I have a lot of conflict with teammates I disagree with”. Your answer is an example of exactly what I’m talking about, something that can be construed as a weakness but is actually kind of a strength because it shows you’re detail oriented.
Also, if you have a good interviewer, they will respect humility. Not all interviewers are good.