Same. First time somebody was trash talking it and showed me how it works I said...That's how I do it in my head.
I'm not a psychologist or a neuroscientist so I don't know if we lose anything by not learning it the way we did in the early 90s, but to be frank, I barely remember doing that stuff. I struggled the last time I had to show somebody long division, and I don't remember the process for multiplying multi-digit numbers on paper at all. It's funny because I do trig, calculus, and linear algebra and convert between decimal, binary, and hex on a daily basis but I can't remember, let alone teach, how I learned to multiply on paper the way I did in when I was 9. I handle it in my head the way you describe as long as there's at least one number with no more than 2 significant digits, after that I pull out a calculator.
I wish I was able to do higher math, I'm one of those that doesn't get it and never will. My brain just doesn't work that way.