Here's some data for you to chew on.
I chronographed 604 five-shot groups with my Howa 1500 .223 shooting mostly SMK 69gr with IMR 8208 XBR and got SDs from 2.22 to 123. Seven percent had SDs below 10. Some of these groups were shot with powder measured with the case activated powder dispenser and some were weighed. Some brass was casually prepared and included plenty of Lake City and Wolf.
With my Savage/Shilen .223 F/TR gun I chronographed 277 five-shot groups with SDs between 2.08 and 80. All charges were carefully weighed using a variety of powder, much of it Vihtavuori N-140, IMR 4198, and IMR 8208 XBR. Bullets were mostly moly coated Berger VLD 80gr or SMK moly coated 90gr. Fourteen percent of the groups had SDs better than 10. All the brass is Lapua carefully prepared
In comparison, my Savage/Shilen 6mm BR Norma shot 195 five-shot groups with SDs between 1.79 and 73, 30% of which had SDs better than 10. Powders were mostly CFE-223, IMR 4895, and IMR 8208 XBR and bullets were mostly Berger 105gr Hybrids, VLD Target, or VLD Hunting. All the brass is Lapua carefully prepared.
You can see that the 6BR gives much better SDs; I guess it's the nature of the beast. It's also easy to see that when I'm careful making .223 competition ammo, the SDs are much better, but still not nearly as good as the 6mm BR ammo. And making more casual ammo for a fun range gun, the SDs aren't as good.
However, and this is important, the SDs don't correlate very well with group size. Here is a plot of several thousand rounds showing both MOA and Group Height vs SD for my Howa 1500 .223 @ 100 yards. The trend line for MOA is nearly flat which means that even horrible SDs produce good MOA numbers and really small SDs can produce very bad MOA performance. Group height shows essentially the same thing.
SD vs Performance
Bottom Line: I strive for good SDs and low ESs. But this graph shows that I worry about it a LOT more than I should.