Mentoring programs like theirs have >5000 students. If they all get the same signal and 10% do the same trade, that can be hard to find liquidity as 500 traders enter the same order.
I don't know how many students they have (that figure is - quite rightly - a closely guarded secret), but I don't think it is in the thousands. If Kim had 5,000 subscribers, then he'd be making around $5million a year just from that and I seriously doubt that. I'm trying to stay neutral here, but stating that I got a lot out of SO, but also highlighting that it is not for everyone. If someone has a big account (>$100K) then it's not scalable, and if someone has a smaller account ($10K) then the annual subscription costs are too much of a burden on the profit.
Also, it required a LOT of hard work - I trade full-time so was happy to watch the screen for hours everyday, but for someone with a full-time job, the returns would be lower.
I agree with the point you raised about everyone piling in to get a fill on the same trade - this definitely was the case many times. As soon as a trade alert would come out the price would rise, as newbies would want to get in, and kept on bidding the price upwards. Kim constantly reminds people "not to chase prices", and many times, after the initial rise, the price would settle back to the original trade alert price, maybe a day or two later. On some lower volume stocks it's possible to spot the options trades that have been carried out by SO subscribers, and in many cases, for particular strikes and expiries, much/most of the trade has been done by SO guys. I myself was responsible for almost all the daily volume on the 11th July '18 in some strikes for BKNG. I traded 315 puts that day, going in and out numerous times. But that's another story......