So your main point is that you want bitcoin to be faster. Great, well done. The reason it isn't faster is that there is disagreement as to how to do it. Increasing the block size was the original idea and would scale without limit.
The number of people a user transacts with in their lifetime is definitely not a constant. We've seen an explosive growth in that number thanks to (mostly centralized) online payments (and micropayments).
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The number of transactions a person makes is not a function of the number of participants in the system. Perhaps it is a constant that grows over time.
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I don't think "constant" means what you think it means.
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