"these days"?
The goal is to memorize single digit products and use the multi-column algorithms when you need to do more digits. To which days are you referring where kids would be called upon to memorize multidigit multiplications?
In the 1980s I had a trapper keeper with a 12x12 table printed on it but even my seven year old ass knew back then that everything >10 was wasteful to memorize. :P
20 years ago my kid still had to learn up to 12x20. The 12s are pretty handy for a bunch of reasons, and especially if you live in the USA. Using base 10 for the metric system was a mistake.
In the US AFAIK they are called "times tables"; in Germany "one times one" („Einmaleins‟). It's funny what people emphasize for the same thing.