"the illusion of control. "
Part of it is closer to delusion of control, but players do have a little bit of actual control over the outcome.
"psychologically and mathematically, this makes perfect sense "
I disagree. This is the one way in which players can have some control over the outcome. While most tickets are QPs the 20 to 30% that aren't QPs aren't a random sample of all possible combinations. By choosing your own numbers you can guarantee that you aren't playing all calendar numbers or a pattern, and you can also try to choose a combination that won't match the other non-random selections other self pick players may be making. You can't increase your chances of winning the jackpot, but you can increase the chances of not sharing a jackpot.
"Humans are notoriously bad at generating true randomness (we tend to spread numbers out visually or avoid consecutive numbers, which actually disrupts true randomness) "
I've always been puzzled about how many people seem to think that they're better off picking a set of numbers that's somewhat uniformly spread over the range of numbers in the game. It doesn't make you any less likely to win anything, but a lot of people seem to mistakenly think it gives them a better chance of winning. You're sort of right if you're thinking "What are the chances the numbers will all be over 40?" but if you only play numbers over 40 you're still playing individual combinations that have exactly the same chance as any of the combinations using uniformly distributed numbers. And that's exactly why players don't need to be good at picking random numbers. Any combination you choose is still random in terms of the probability that it will be chosen. Sure, the the winning combination probably won't be all numbers over 40 but that's only because there are fewer possible combinations with any subset of possible numbers than there are with all of them. If there were prizes for playing a combination that had the same characteristics as the wining combination then it would matter, but the chances of the winning combination being drawn will be the same regardless of how the individual numbers are distributed across the numbers you can choose from.
"This reflects the deeply ingrained human desire to find patterns in chaos. "
Just because the conditions that cause the results are chaotic doesn't mean the results won't show some kind of pattern(s). The mistake is thinking that the patterns indicate that the process isn't chaotic or random and that any (past) patterns offer any useful insight into future results.
"The fact that the number 7 was drawn last week "
Aside from past results being irrelevant to future results, "the number 7" is never actually drawn. Sometimes a ball with "7" on it is drawn, but the next time a ball with "7" on it is drawn it's most likely a different a ball than the previous time. This one is another example of normal human behavior in attributing characteristics based on a misunderstanding. Similarly, nobody has ever come close to matching a winning combination because the numbers on their ticket are "close" to the winning numbers. Even if each of the balls with the numbers you played started out right next to the balls that were selected they stop being close once the balls start mixing. The real balls that were close were the ones that were closest to popping out when the winning ball popped out. For an RNG game, whether the the selection is truly random or not, we can never really know what was theoretically close because a 7 has no proximity to a 6 or 8 in the RNG process. Close would be whatever combination(s) might have been produced by using whatever seed might have been used immediately before or after the seed that resulted in the winning combination.
"People who play the exact same numbers every week enter a psychological trap "
There's your next poll if you want to give it a go. I see plenty of posts from people who think they need to have a chance at every single drawing, and I'm sure that includes plenty of people who don't use the same numbers, but I expect there are also people who play the same numbers but don't feel a need to play every drawing. I'm one of the people who use the same numbers for an extended period of time, but I don't play every drawing. For PB I don't play until the cash value is $250 million, so the last ticket I bought would have been for the Christmas eve drawing. At $5 the comparable MM entry point would be a cash value of $625 million, but in most recent years PB has offered a few chances to try for a cash jackpot t hat big for only $2. I won't know what my entry point for MM is until I buy a ticket, but I'm thinking it has to be somewhere north of $750 million cash. Even then, if MM is offering 750 or 800 and PB is offering perhaps 600 I'll figure I could be about twice as likely to win almost as much and save $1 compared to buying the MM ticket.