Here's a different perspective.
Highly accurate target barrels are made to extremely close tolerances by their makers. Something like .0001" or .0002" in the bore. They are hand lapped to meet this spec, and those that do not wind up as fence posts!
In the past, it was impossible to industrial hard chrome plate an object and hold this kind of tolerance because 1) the technology just did not exist, 2) the process is a relatavely expensive one for the small low volume maker to experiment with improving, and 3) there was little to no demand for an expensive barrel that couldn't be made to equal or better the existing standard. Add to this the fact that the available hard chromed barrels were already acceptable for their most important use (the military) and you can see why no real development was done on them for decades.
This has all changed with the new process developed by FN and first used in small arms on their LMG's. The SPR barrels were .30 cal MG barrels taken from the line and shortened and profiled for the police rifle. As I understand it this is a very expensive new process that FN has come up with, and I suppose that they own it and any potential user would probably have to pay licensing fees or royalties to use it. My safest guess is that we'll just have to wait and see how this shakes out in the future.
I believe that the Springfield story is just that. Our military teams have been using custom barrels, first CM then SS, for decades. The old star gage and then air gauged NM Springfield barrels have not been used by our military MUs since the 1950's.
So, to break-in or not? First, I would advise to strictly follow the barrelmakers reconmmendation not only on break-in proceedure but also on what cleaners, etc. to use. Lacking that information, if the barrel is CM or SS break it in! Do a search and you'll find several good methods, just choose one that suits you. If you've got a new chromed bore barrel, go ahead and shoot it as is. The hard chrome is harder than anything that you're about to put through it anyhow.
The reasons for break-in on machined metal surfaces are a subject for a completely new thread. Don't get me started, please;-))