Firing pin springs vary from manufacturer to manufacturer. To say bolt guns don't like hard primers is a very broad, and often incorrect, generalization. From personal experience, Savage and Browning rifles seem to have the most problems with hard primers so I would guess they use weaker firing pin springs than other makes. Some Savages work great with hard primers though so it may be a rifle-to-rifle thing to check yourself. I've not heard of a Remington bolt rifle having issues with hard military primers and mine in 308 will fire the hardest primers with ease.
Few if any off the shelf bolt rifles have a short enough throat to worry about 5.56 vs .223. Savage rifles actually have longer throats than 5.56NATO chamber specs. Only the tightest chambered, bare minimum throat length, match cut chambers will cause issues with 5.56 ammo. 5.56 and .223 actually have almost identical max chamber pressures when using the same measuring technique and equipment. 5.56 is meant to produce the assumed pressure in a NATO spec chamber and a tighter chamber or one with a much shorter throat can cause pressure to rise. Most .223 ammo is designed to produce near the max pressure in a very tight, near minimum spec chamber which is almost never the case in non-custom rifles. As a result .223 often produces less than max pressure in common civilian rifles.
Most quality or match .223 ammo will cost over $1/round and can be reloaded for less. If you're looking to shoot a lot of match ammo, I'd look into reloading. If you're looking for bulk plinking ammo, buy a couple boxes of several brands of cheap steel cased stuff and see if your rifle will set it off reliably. If it does, buy a case.
