OK... I've been shooting and hunting with lightweight rifles and I've been primarily a light rifle shooter for over since I got my first Remington 660 in the mid-seventies.
I see NO problem with shooting a light rifle accurately but then that's what I'm used to. I've found proper bedding of the action and often the full barrel channel as well to be critical with the lightweight rifles. Triggers set at 2 pounds or lighter are needed as well.
The Remington Custom Shop, before they moved from Ilion NY, made a LOT of lightweight Model Seven rifles called the KS model with 20" barrels and if you can get one of them with the original McMillan or Brown Precision stocks you'll have a sweet rifle AFTER you have it bedded properly and get the 40X trigger they came with adjusted down to 2 pounds. Beware... Remington greatly cheapened this rifle when they left Ilion and many of their older more experienced gunsmiths either quit or retired to avoid moving.
The barrel taper on these rifles is nothing like any other I've ever seen come from Remington and it's a much heavier taper than any Model Sevens I've seen other than the Alaskan (NOT American) Wilderness Rifles. IIRC they (KS's) weighed in right at 6 pounds sans scope and mounts.
That brings us to the original Remington Model Seven Alaskan (NOT American) Wilderness Rifles. They came in several chamberings but the only ones I've ever owned are the 7mmSAUM and 300SAUM and these weigh in at around 7 pounds with a McMillan AWR Stock and teflon metalwork coating over the stainless metal. This coating scratched very easily and therefore looked horrible but that's the way you can tell that you have one of the original AWR Custom Shop rifles. Barrels were 22" with a unique magnum taper and accuracy, after you get the bedding right, is usually close to a half inch at a hunnert.
I don't know if these rifles I've mentioned are "better or best" because that's so subjective and you rarely if ever see one of the KS's or a real Alaskan Wilderness Rifle for sale any more. Most of them are in the hands of collectors and hunters that covet lightweight hunting rifles and if you don't know what you're doing, you'll end up with a cheap imitation like today's Remington American Wilderness Rifles.
By the way... I completely disagree that anyone can build an accurate lightweight rifle. I've owned a bunch of different ones in my life and very few were capable of better than 1.5" at a hundred and many were more like 2-3" at a hundred with little that could be done to help. Barrel contour in lightweight hunting rifles is critical and you need ultralight actions and stocks so you can spend your weight allowance on the barrel where it's needed MOST!!!