I'm sorry I couldn't help but nerd out. Oops. TL;DR: at the end. Caveat: not a climber, not an expert, don't know if 300 is accurate as a regular thing, BUT:
You can't summit Everest every day or even nearly. There are hundreds of days every year where you couldn't summit, and even if by some miracle you did, you'd find yourself on the highest point of the world and facing down a monsoon or a jet stream. (I don't know if there's a chance you'd ever face both? I don't pretend to understand all the ins and outs of the weather.)
When Krakauer's team were on the South Col in the '96 disaster, the winds were literally hurricane force and blowing their tents apart. So even in the right season and on days considered suitable for summiting, conditions can get deadly very fast. And the camp on the South Col is still in the death zone, to my understanding, so you're talking potentially deadly weather in a situation where without supplementing oxygen (arguably even with it?), your body is actively dying. I imagine the jet stream would just whisht you off that mountain. And camp four is still a ways from the summit. You're spending multiple days in a place which is passively or sometimes actively trying to kill you. Those are the conditions in which you're waiting for a day when you might reasonably reach the summit.
There's a window in late April to late May called Everest season for a reason; I think the actual summit window is way smaller than a month though, and then you have to pick a day and hope the weather is good to you. There's also a window in autumn but it's much shorter and most people who summit Everest (especially those who are inexperienced at those altitudes) will be doing so in mid to late May depending on the weather. And suitable weather is a moving target - even in ideal conditions, you're still in the death zone, you're still freezing and actively dying, there's still wind and the possibility a storm could blow up and kill you out of apparently nowhere. (Most of the people who die on Everest are still there, because it's expensive and dangerous to bring bodies down and risks even more lives. Some people do eventually get retrieved, but there have been bodies on Everest that are effectively landmarks that dozens or hundreds people have climbed past or even sheltered near. Apparently there's somewhere just below the summit known as Rainbow Valley because of the number of bodies in down jackets in many bright colours that are still lying there.)
Also note that some parts of the route are bottlenecks and can only be climbed safely one person or group at a time, so on both ascent and descent, there's a non-zero chance you are going to have to stand around in oxygen-poor freezing-to-death cold air while someone else comes up or down. I believe the ladders in the ice falls are generally taken one at a time, and I think the Hillary Step was a bit of a bottleneck before it was destroyed. I'm absolutely sure there are others I've forgotten or am not aware of.
So yes, you are absolutely correct that there aren't 300 people summiting Everest every day, and there are hundreds of days a year where no one is up there at all. There are, however, sometimes hundreds (or at least dozens) of people climbing Everest on the same day in mid to late May and that's when you get pictures like this:
There were apparently 320 people attempting to summit 😬
Basically, weather conditions x people paying to Do Everest™ = you have a lot of people attempting to summit in very short timeframes along the exact same route, and that's when you end up with these absurd traffic jams on a mountain that, let's be real, most of these people shouldn't be anywhere near.
(Again, not a climber, but to my understanding, the climbing on the North and South Col routes on Everest isn't the problem, it's not very technically "difficult", it's the extreme conditions that are the issue. Something that would be easy peasy at sea level can be rapidly deadly when you are hypoxic and exhausted and freezing, and also possibly have picked up something nasty before you even hit base camp because the conditions at some of the lower down bottlenecks are also actually appalling. And sometimes things that would even be survivable on Everest turn deadly, sometimes even because of these same crowds. Maybe on one day you could summit and make your way down to camp four without interruptions and grab another bottle of oxygen just fine, but if it's a different day and you're caught at the top of the Hillary step for an hour waiting for people to come up and you get that much colder and that much more oxygen deprived? And that day, you stumble or take a wrong step or are just too exhausted to keep going, and now you're dead, not because of the mountain directly, but because there were too many people, so you stayed at high altitude too long with not enough oxygen.)
TL;DR: No, there absolutely are not 300 people queueing to summit Sagarmatha every day, but unfortunately because of the narrow window to summit x a lot of people on the "easy" routes, there are also times when that is literally true.
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