OP has a CL barrel, so just run a patch thru to catch production/shipping debris and shoot til it's dark.
However, Krieger SS barrels are worthy of their specific instructions to break in, running a patch after each of the first 5 rounds, then after several groups of five, then after ten.
The reason Krieger gives is that after the rifling is CUT (their barrels are cut rifled, not buttoned) and the chamber is cut, there are microscopic stainless steel shavings left in the barrel. when a copper jacket is sent down the pipe at 2800 fps or whatever, the superheated copper bonds with these fragments, causing unevenness near the throat.
This causes a higher rate of copper buildup as the rifle is used, which in turn leads to more rapidly diminishing accuracy as the rifle ages, or as its daily/match round count progresses through a long match day.
For my Kriegers, I've always followed the instructions, and have always had excellent results. What's an extra 30 minutes of hassle for a barrel you may own for a decade?
But with chrome, fuggedaboudit.