I have barely sold anything
What you are describing is a buy and hold strategy with individual stocks.
It's already better than the sort of active trading that tend to produce returns significantly worse than the market index.
At one logical extreme (buying and holding stock of hundreds of thousands of individual companies), you've basically just recreated an index fund and should have about the same expected return and variance as an index fund.
As you move towards the other logical extreme (buying and holding the stock of a single company), your expected return stays the same, but your variance starts to increase. In any given year, some sets of 5 companies will have returns that are much higher than the market as a whole, and other sets of 5 companies will have returns that are much lower than the market as a whole.
Did I just get lucky?
Yes.
Is the simulator missing extra fees and taxes? (the fee is worked into the original stock purchase, and
there is no mention of taxes)
Potentially, but those don't make a big difference over short time frames like this.
I hear people all the time say that it's hard to pick winners. I have mainly
stuck to the established leaders.
It is hard to
consistently pick winners.
What are the pitfalls to stock picking that I am not seeing with the simulator?
That, even with buy and hold, about half the time you'll under perform the market, sometimes by a lot.
When I first got interested in investing, I did some individual stock buys. At the time, peak oil was the watchword of the day, and I talked myself into putting a lot of my early savings into a handful of oil company stocks assuming the value of their proven reserves would continue to increase because "they aren't making any more of it."* I was beating the market for quite a while, AND collecting better than market rate dividends at the same time.... until I wasn't anymore.
They say the worst thing than can happen for somebody with a propensity to gamble is to win the very first time they play.
*Generally this is an argument people use to try to convince you to invest in real estate, but same logic (or lack thereof) applied here.