My experience is Savages were easy to work on and customize with the barrel nut and floating bolt head as a DIY tightwad. Not as robust aftermarket as the Rem 700, but plenty. You can take a long action Savage from .223 to 300 rum if you want. That's a huge plus.
A Proof prefit barrel on a frankensavage shot just as well as the same barrel in a custom action, custom stock, and trigger (that cost almost as much as the Savage action did, lol). Barrels are the biggest part of the accuracy equation.
Of the gazzilions of cheap Savages out there, yeah, extractors definitely go down. The cheap upgrade fixes it most every time. I never had a problem with like 10 or 12 I owned or half dozen other friends have.
Yup, the primary extraction is goofy and bolt timing can be way off making bolt lift crazy. And, the bolt is sloppy for sure.
Yes, on a new rifle you should pull every bolt, degrease it and retorque it. Probably a dozen times I have helped a random guy struggling to zero a new Savage with the factory scope. Invariably the rings and base are loose. Add blue loctite and torque and they are usually good to go. Their frustration changes to elation when they shoot a very good grouo.
The Accutrigger is one of the best factory triggers out there for precision I have felt. It won't hold you back until the typical shooter's form is greatly improved. It is functionally like a two stage. It is also a pretty decent safety feature.
I don't own a single centerfire Savage any more, and probably won't buy one. But, "for the money" your odds are much higher getting a good shooter.
Its pros make up for the cons to a big subset of buyers and shooters. The cons turn off a bigger group.