Military primers

No reason at all.

They will be a bit harder which should only matter if you have replaced the factory springs for lighter ones.

My Savage model 12 has trouble setting off the military primers. Maybe 1 in 10 won't fire. That can get nerve racking. Your bolt action may not have that issue but it's something to consider before you load up a bunch

Some commercial bolt-action rifles don't have a strong enough striker spring
to consistently set off mil-spec primers.

Many years ago I ran into this with a Ruger MKII in .308 Win.

Replacing with Wolff extra power spring resolved the issue.

Later Ruger changed the factory spec to heavier for the same spring.
Guess they realized the issue too...

My Ruger American Ranch 300 BO does not like Military or even thick Magnum primers. So I usually just stick with cci 400's . I have a 300BO in a AR and used cci 41's and they were very iffy in the Ruger. Now I just use 400's in both to avoid confusion.
Load up a small amount and check.
Josh

Unless the springs on your gun are totally wiped out I highly doubt you will have any problems with those primers. You can use them in bolt action rifles without a problem, they are only slightly less sensitive than standard primers.

One thing to consider. The NATO primers from CCI are magnum class primers so load them accordingly. If you are at the very top of the pressure range with a standard primer you will want to drop back a bit and work back up. That is true though with any component change.