I dunno if I'd say the centerfire Target Action is any more "serious" about accuracy than a standard repeater action. They all come off the same machines and are machined to the same tolerances and are assembled with the same parts, so they're no more special or accurate than a Stevens 200 action in that regard. You just pay a premium for an overly sensitive Target AccuTrigger, and band-aid fixed bolt handle and the "Target" in the name (kind of like how anything with tactical in it's name costs 20% more).

As for a serious target rimfire, Savage has been approached with just such an animal but thus far they haven't shown any real interest in it.