I actually was taught this and a number of other "tricks" in primary school. Estimation was a defined thing, and the idea of getting quick math results in your head was a real goal. Reasons given: job interview, pricing goods and services to understand value, fuel consumption, making things (that deck, how many boards, cost, etc...), navigation.
They took us through a lot of those cases. The first time I applied this was powers of 2 for computing. Learn the first 16 bits worth, and that helps with all sorts of things in computing, same as powers of ten and common easy to compute things do in most other areas of life.
So, what I did was make it a car game. Figure out how tall things might be, or prices, whatever comes up. Practice doing it helps to actualize the skill and once it's done, they will apply in in ways they find useful.
Instead of memorizing algorithms, kids should be shown this. It's free gamification and, after some years, I believe it's a core idea of what is, and why math can be pleasing.