I learned all about this in "thinking fast and slow" by Daniel Kahneman. He talks about system 1 and system 2, where system 1 is your kind of knee-jerk reaction to a thing (thinking fast), and system 2 is the contemplative and careful consideration of a thing (thinking slow).

I would argue that some people overly leverage system 1 (thinking fast) because it's generally easier, and takes less time and mental effort to do. Those that either can't, or are unwilling to engage system 2 in their day to day activities, will 100% fall for these kinds of misleading prices, since system 1 is cutting so many corners so that it can be fast and efficient (mostly on how much energy is used), that it skips a lot of the cognitive steps and goes right to the (often incorrect) conclusion. That $19.99 is $19 (or $10 in some cases).

In the book, they discuss that system 1 often gives the wrong information that is later rejected my system 2 when further consideration is given to a particular input/stimulus.

If someone isn't engaging system 2 as a check to ensure system 1 isn't lying to them, then shit like $19.99 seems cheaper than $20. It doesn't hold up to any scrutiny, but they're not targeting thoughtful people with these practices. For thoughtful people, there's functionally no difference between $19.99 and $20.

Yes, the difference is one cent, but given that one cent is so worthless in today's society, to the point that Canada stopped making one cent coins (and other countries have done so as well), there's functionally no difference between the prices.

One cent is only worth anything if it is combined with many other cents. The sum of those pennies becomes valuable when you conglomerate enough of them.