i have not usually agreed very much with you in the past but you are spot on about this

the mathematical principle that governs this is called a "poisson point process" and this is the same thing that is in play with radioactive decay and other types of half-life, for instance, use by dates are calculated on this basis, in drug testing a standard preliminary test is the LD50, which usually is done with lab rats, who are most physiologically similar to humans, and the number is based on the dose that kills half of the test subjects - lethal dose 50%

in chemistry the principle is called "mass action" and more generally is covered by the subject of "probability"

your chances of winning a block are literally one in a million, you don't know which of that million it will be, that's the poisson part, but there is 144 blocks per day and there hasn't even been a million blocks yet

the logic of pooling is very clear, it is a risk-sharing system where everyone's contribution is measured in some secure way and the amount of contribution you make to the number of attempts on a block are counted as your share and your reward matches that proportion

it essentially eliminates the "lumpiness" of the distribution of your chances of mining a block and gives you a regular reward based on the amount of work you are contributing to the pool's work

it was one of the things that was beneficial with PoW schemes with short blocks (like ethereum's minimal 15 second block time) - that's a lot more chances for a solo miner to actually get a block in a short period of time... but there is other downsides to such short block times, latency being a big problem there, because while 12 seconds is the average block propagation time (as in, if you win a block but someone else did at the same time) then it's about which block reaches the network's majority first, because that is the one that gets at teh head of the block and becomes the new best block

you probably also know that the occasions at which two miners find a block within a short time period of each other is surprisingly high, and the shorter the block time target, the more likely such a collision occurs - this is why bitcoin's block time is 10 minutes, this reduces the chances of solutions coming at less time than the minimal average latency distance between them

which also means that bitcoin mining has to go to pools sooner rather than later, in order to be economically viable

solo mining is fine, and fun and all, but if you are doing it, keep in mind you may be waiting literally over 15 years to get a block, and that's a lot of time and power bills to pay in the meantime