Over the long run, (assuming no difficulty changes) all pools will generate the same amount of BTC. The problem is that if a small pool has even a little bit of bad luck early on then the miners will likely never recover when taking into consideration difficulty increases.
That's true. But on the other hand, if you have even a little bit of good luck early on, the bad luck later on won't catch up.
In the end, it mostly averages out. The average outcome (expected value) under exponentially increasing difficulty remains the same for all pool sizes. The variance (randomness in the total btc after N months) is only slightly bigger compared to constant difficulty (and, as always, is higher for smaller pools).