Honestly I feel like I do the same thing when I think about it, but it’s so well cached that whenever my brain sees 5+7 or 7+5, I simultaneously think “12”, forget the specific order, and imagine 5+5=10 with 2 overflow all at once and I can’t honestly tell you which concept arrives first.

And yeah, you can get by with less memorization and more counting, but eh...either you’re taught not to do that or you do enough arithmetic that your brain just caches the whole table eventually anyway.