Well, my experience is that if you don't wait a bit, and just add a
bunch of fish to a completely new tank, you'll get a NO2 spike which
can be deadly to the fish, especially if they're already sick. Of
course, adding existing filter media solves that problem since that
introduces enough bacteria to get started. Using water from a running
tank also does that, but there aren't a lot of nitrifying bacteria in
the water, more in the filter and the ground substrate.
On the other hand, I believe you do weekly water changes? That of
course also helps in avoiding the NO2 spike. But I've read a lot of
stories of people (on dutch forums) that buy a tank, fill it with
water and put a dozen fish in it (all on the same day) and think that
everything will run smoothly for a month or so before they have to do
anything else. Well, it won't...