Another reason to rotate questions more frequently and maybe a reason interviewers raise their standards over time is because there are large forums out there dedicated to cheating and sharing solutions for any notable tech company. As more and more questions are shared more and more cheaters will perform optimally, raising the average performance for that question.
I could tell you which questions were asked at MTV this past week and by looking at the last month of these posts for a specific office it's incredibly easy to come up with the most frequently asked questions and memorize their optimal solutions. This means that if you're someone who doesn't partake in these communities that you'll enter these interviews at a significant disadvantage because your performance on that problem will be compared to everyone who was able to (legitimately or illegitimately) arrive at the optimal solution in 45 minutes.
At Google, questions are chosen out of a predetermined question pool. It doesn't matter how many interviewers there are. It's small enough that your interviewers leave a note on a piece of paper at the end of each round indicating which question they picked to ensure no two interviewers ask the same one. The question pool changes over time, but it rotates much slower thank you would think. Furthermore, even having an idea of the "theme" is a huge advantage given the variety of topics that can be asked.
I work at Google and conduct interviews there. There is no pool of questions. Interviewers are invited, but not required to share their questions with everyone else, but not all do, and there's no approval process for them. I don't know if what you're saying ever was true, but it certainly hasn't been for the past ~5 years or so.
I can only speak to one office so I shouldn't have assumed it was the case company wide. I only know two things:
1) At the office that my friend (who is also an interviewer) works, there is a pool that the interviewers collaboratively built and generally select from. They aren't required to choose from this pool, but 95% of them do because they contributed to it.
2) At MTV there's either a pool or the number of interviewers is so low that the same questions are repeated over and over at high frequency for several weeks, making it trivial to know which ones are likely to show up. I know because the questions I found on the sketchy Chinese forums were exactly the ones I encountered on my onsite interview.
As an alternative to 2, you just got lucky. There's lots of interviewers and lots of questions. My office is smaller than MTV, though not by much, and I don't think I've seen the same question come up more than a handful of times.
I'm unclear if 1 is referring to a specific office pool, which would be weird, or the global knowledge base I mentioned, but that has lots of questions, more than one could hope to memorize in any reasonable time frame.
So, there's a pool insofar as, like I said, there's a thing you're invited to add your questions to. But you aren't required to ask questions from the pool (and I know many people who don't). And also the "pool" is huge, which is different from some other companies I've interviewed at, where interviewers are required to ask questions from a small (~10-15), preselected set.
Problem with your approach is in order to make sure your made up problem isn't banned you have to go through all the banned question everytime you ask your question. That's a lot of unnecessary toil.
I could tell you which questions were asked at MTV this past week and by looking at the last month of these posts for a specific office it's incredibly easy to come up with the most frequently asked questions and memorize their optimal solutions. This means that if you're someone who doesn't partake in these communities that you'll enter these interviews at a significant disadvantage because your performance on that problem will be compared to everyone who was able to (legitimately or illegitimately) arrive at the optimal solution in 45 minutes.