You might not like it, but that trigger movement doesn’t (or shouldn’t) show up on the target.
It's definitely a preference thing for me. Accuracy wise, I can get what I need from a stock Savage trigger, but that doesn't mean I like them. The only reason for me to build the rifle with a custom 700 clone is so I can put a trigger in it that I really like. Otherwise, I'd just find a Savage 110 on sale somewhere for $300, buy a new stock for it and a new barrel in my choice of chambers and call it done. Short of the 1813 smallbore and my 2002 Anschutz air rifle, everything else I've ever owned has been what I would consider "entry level".
For most disciplines, I've found that entry level equipment is more than accurate enough to win matches at the state and local levels. Points that I've dropped are because I dropped them, not because my equipment was insufficient. I've always wanted a custom rifle, but its never been in the budget. When we started a family 20 years ago, I quickly ran out of time for competing, so my dream of a custom tack driving target rifle quickly faded. I still hunt and do some plinking and training for fun a few times a year, but not enough to justify the cost of something like that.
Once our house was paid off, I was able to set aside a little money once in a while. After a while I was able to picked up a Savage 12FV from cabelas in 223 just to see if I thought i could ever be happy with a rifle built on a Savage action. Cheap rifle to feed, and no complaints on the accuracy. Straight from the box it was capable of 1/4 moa with hand loads. I really have no complaints about the rifle, but if I'm going to plan on spending well over a grand on a rifle, I WANT a trigger that I enjoy a LOT more than this.
A few years later I started doing a somewhat anual trip west a few years back for PDs. In an effort to enjoy the Savage moor, I put a timney trigger in it and dropped it in an Oryx chassis. As a 300-400 yd pd fifle, it's fine. One heck of a rifle for the $$, but I just can't get myself to enjoy the single stage trigger. If I'm going to build a rifle from scratch, I'm not going to be happy with it unless I can set the trigger up the way I want it. I'd gladly spend the money for an anschutz trigger if I knew I'd be able to fit it in a common chassis (or a stock I like) without dealing with a ton of headaches, but I'm not willing to drop $600--$700 on it without knowing it will end up working for me in the end. Similarly, I don't want to drop $300-$400 on a trigger I know will fit in the rifle without knowing I can set it up the way I want it.