This is my experience; cases with belts can be just as, if not more, accurate as non belted cases.
I have been shooting F-Class Open for nearly 15 years with a 300WM, this round has been surpassed by some bigger, but mostly smaller rounds, but to me is still number 1 for it's accuracy.
I recently built a 338Edge, it's still in the load development stage, but so far isn't any more accurate than my 300WM. It does have an advantage with wind drift, but group sizes so far are about the same between the 2, around 9"-10" on a good day.
I have a Win Model 70 EW in 338WM, it puts 3 shots into a ragged hole @ 200yrds consistently with Nosler 225gr Accubonds, it is very accurate out to 800yrds, but I do not shoot it at that distance often, other than informal target practise on my private range. I also have a 375 Weatherby that shoots sub MoA groups regularly with a few bullet weights.
My other super accurate rifle is, apart from pillars and a very good bedding job, a Ruger M77 MKII with standard semi heavy barrel in 25-06. It consistently shoots 1/4 MoA, it surprises everyone who shoots it how accurate it is. It doesn't have a belt, but is in 'magnum' performance range.
There are more steps/details to consider with the belt. Simple as that. Not including or considering the steps or details of the belt will hurt accuracy but not considering steps or details for any thing will hurt results. Not just firearms.
Before I learned this I feared belted cartridges. I am new to them, so new that I have not even reloaded one case yet, but will soon. I am a very experienced non-belted cartridge reloader and build accurate ammo. I have learned enough from reading on die set up that I will not have any difficulties and will produce accurate ammo, this I am sure of.
I am like Greyfox, in that I've never been picky whether belted or non-belted. I have lots of belted, non-belted, rimmed cases, etc... Never had but 1 problem, and it was related to crappy old work-hardened brass, and not because it had a belt on it. Once I bought more (better quality) brass, I had no more issues.