.223 55 grain

Define "very accurately". There's a reason they're cheap.
My Tikka T3 is sub-minute with almost everything.

Generally, 55 grain FMJ bullets are not as accurate as other bullets because of the open lead base of the bullet. Hollow point or soft point bullets where the jacket closes the base are more accurate.

Having said that, my best score shooting Service rifle on a 100 yard range was done with 55 grain FMJ bullets in an AR-15 rifle. Not a great score, at Marksman level, but still my best.

I generally shoot ballistic tip bullets in my 223 Remington bolt rifles. For plinking in my AR-15's, the 55 FMJ's are great.

Generic 55grn FMJ isn't designed to be benchrest stuff... it's designed and manufactured for service rifle accuracy and reliability. They can be reasonably accurate, and, with any ammo, there is always the chance of a Magic Combination, but I wouldn't normally expect the accuracy I think you are looking for. FWIW, something dedicated to shooting 55grn .22's accurately would have a twist rate to match... and likely not very versatile with other bullet weights.

The most accurate rifle in the world won't shoot well with inaccurate ammo.

^^nailed it.

I've had decent groups with PMC full-jacket. Not exceptional, but generally near one MOA.

Ruger 77 Mk II, light sporter; Timney trigger and an ancient 3-9x40 Leupold. Half-MOA with handloads.

I've seen Hornady fmjs do very well. Everything else runs 3 moa for me.
Just changing to the cheapest factory 55sp gives me <1.5 moa.
Hand loads are a different story.

Yes, but they were my handloads tailored for a Savage Axis. My avatar is some of the results, with my son shooting it.

When I ran out of handloads mid season last summer I grabbed 5 different brands of 55 grainers and ran them through 2 rifles. Differences were 1.5" to over 3" for 5 shot 100yd groups. Picked the best and bought enough to get through the season.

As others have mentioned, the inexpensive production of 55gr FMJ bullets is a major factor in the lack of precision... and Hornady 55gr FMJ and 55gr SP ,have an enviable reputation for being great 55gr "bulk" bullets.

When it comes to FMJ, I've had good luck accuracy wise with Hornady 55s and 62s.

Both will hover right around 1 MOA in a couple rifles with limited load development. Plenty of accurate for 3 gun matches and an occasional class. When accuracy really counts, I use Sierra OTMKs or TMKs and for yotes Nosler BTs.