But, they all gain from the lower variance, as more trials in the same wall-clock-time means better convergence to PPS-like payouts. So to the extent subscribers to the gambler's fallacy do jump in after unlucky periods, they reduce variance just at those times when it becomes embarrassing to the pool. A simple graph that obscured hashrate changes over time might make such a pool look unnaturally lucky.
with pplns there will be timely long rounds too, because of a lot of hoppers. the abandonment problem just shifts from the end to the beginning.
in prop every hopper leaves to the end so the speed gets slower with time.
with pplns the speed is directly slow at the beginning because everybody leaves after the round is completed. and as no shares get completed no hopper rejoins. and as the speed is crippled, normal ppl propably won't join too, because they won't get paid in a long time. crippling the pool even further.
Your analysis seems to assume there's some benefit under PPLNS from hopping in and out, so a lot of people will do it. There's no benefit, so it will only be a small group of superstitious people.
At most, when a lot of people join, the variance goes down. That's the same for every pool and payment scheme, more participants equals more frequent but smaller payments. It always attracts some people to the largest pools or those they expect to be largest.
If irrational superstitious hoppers make a PPLNS pool larger when there has been a long period without a generated block, that just makes the pool more attractive to rational variance-minimizers and fuss-minimizers, seeking a fair pool requiring minimum attention.
So lets say the hoppers leave after a generation in a futile search for higher returns elsewhere. Note that they are then increasing the variance of their still-alive PPLNS shares so this hop is even worse than neutral for one possible goal.
Some of the variance-minimizers and fuss-minimizers who joined during the hopper inrush are likely to stay. Each seasonal cycle of irrational hoppers should leave the pool with a larger base. And slowly train the hoppers to stop wasting their effort.