I don't know if it's cultural, but as someone of the 'current generation' (Gen Z), I feel that the opposite is true and typing speeds increase as you get younger (to some limit).

I've tried to back this up and only found a single, questionable, data source[0] on the topic but I do attend several typing competitions and some of the young ages are phenomenal. I was beaten a few months ago by a 15 year old who was typing >220wpm+ for 5 minutes.

[0] http://drwes.blogspot.com/2011/01/results-are-in-age-vs-typi...

I'll second the other Gen z person in the replies and say that lots of us hate thumb typing and if we're going to generalize across every single living person by one factor, my experience is that typing speed goes down with age.