According, to a bit of research I've just done you've been slightly lucky when it comes to hitting 2s. The best starter word apparently should give you a 2 in 6.5% 6.5% of games.
I think my average of 3.98 shows that this luck evens itself out!
I do stick with the same starter word now, after flirting with a few different words in the early days. If my starter ever comes up as a 1, I’ll retire it and use another.