Proof-of-transaction incentivizes users from an early stage to join a harvest club with the most harvest power. Because of this, it is unlikely that by the year 2040 there will be several thousand separate harvest clubs, as it is likely that one of the early large harvest clubs will become a majority pool, sucking up most of the new users that enter the network. In my estimation, by 2040 there will only be a few very large harvest clubs.
Potential resolution: Limit the number of members per harvest club to ~5,000.
Potential resolution 2: Require a physical authenticator for transactions.
Very deep insight into the mechanism.
I'd like to mention that the harvest power of the club you join doesn't affect your expected harvest reward, as long as the club is always harvesting. Harvest power and reward is exactly in linear proportion to transaction count. For this reason, putting limit on a single harvest club probably will not work, since splitting one harvest club into two will not change its combined harvest power (exactly the same chance of generating new block).