I think you missed one small point. That 1 million stat is per month. Not per week, day or god forbid hour. LoL servers can't even deal with that, we have had waits to get into the game for URF before the rotating game queue.
So try your math with the assumption that I play a lot of League. I don't play monday or thursday except the very rare single game when I just need a break from my college workload. Wednsday I don't play a lot either, but usually get a game or two in. Thursday and Friday I have work, so I don't play until around 5 pm. I then play maybe 5 games each day.
That puts us up to around 12 games before the weekend, and over the weekend I play a lot of different games so I get anywhere from 10-20 LoL games in. All told this means I play an average of 27 games per week, but lets be generous for your argument and say it is 30, well above the average number of LoL games per week.
Each game takes 20-40 minutes on average, meaning that is 30 minutes. I tend to spend 1-5 minutes in queue per game, so lets say that comes to 35 minutes per game as I am a support player and as such get short queues.
That means that per week I spend 1050 minutes playing LoL. In a month I spend 4200 minutes. We can take this as a high average for LoL players. Our 1,000,000 players spend 4,200,000,000 minutes playing LoL per month.
In 1 month there are roughly 42,000 minutes which is really convenient for my math. The average LoL player thus spends 1/10th of their life playing LoL. Wow, I mean I am guessing high so you can't call me out on my math not favouring you here but that is just sad.
Anyways this means that on average only 1/10th of the LoL playerbase is attempting to play a game, this equates to 100,000 people online.
That leaves 50,000 for all the higher queues, and you did the math for that (which I appreciate by the way.) That being said your math was off, you don't divide by half. Masters+ is only .08% of the LoL playerbase which we can directly break into 800ish players from the total 1 million, meaning you only have 80ish masters+ players on at a time.
Except it doesn't.
You see that 1 million stat? That is across all regions. LoL doesn't have one region, it has 10 servers. This means that taking averages we get another 1/10th of the people in each queue, dropping us to virtually no players at high levels of queue, which is the big reason why people complain when they get matched vs people of other ranks, each server is independent and we don't have that many players per server.
Hell I have experienced this, I ranked Gold last season and I got flung in with a challenger player in normals, it happens. Challenger players are actually a bit more common than that because they play more than most LoL players, but even then we are only hitting like 20 masters+ players online at a time per regions. Once again, not as bad as it sounds because per region they all tend to be on at close to the same times, but that means that during the downtimes there are even less of them on.
1 million players sounds like a lot, but when only about 1/10th of them are on at a time, and only 1/10th of those are on each server (on average of course, NA has more, Oceana has less for example) we suddenly only have 10,000 people in a region playing the game and when over 75% of them are Bronze-Silver that leaves us with 2,500 in Gold+. That just isn't a lot when you have to split that across every game queue.