Very slow stick (extruded) powders have a lot of deterrent coating, to slow the initial burn. A large capacity case like a 300 or 338Mag would use a very slow powder. They are more reliable with a magnum primer. In my experience they worked well with standard primers, but I don't know how close I was to failure. Cold weather might have been an issue.
Ball powders are harder to ignite. they need flame and pressure to ignite reliably. If you want to explore the world of poor ignition, take a medium sized case and make a mild load using ball powder and a light bullet. You can get misfires or click-bangs.
The solution with any load using ball power is a stiff charge of powder (almost full case), a heavy bullet and some crimp. This will ignite just fine with a standard primer. If you can't satisfy one of those criteria, use a magnum primer to be sure of ignition.
The fact that you ammo has always worked is not proof a standard primer is ok. All it means is that is has always worked, so far. One day a rifle with a lazy firing pin spring, some oil and some cold weather will cross the line and it won't fire.
If the case is full of powder, the primer makes enough pressure to pop the bullet out of the case, into the throat. This can really bugger up a hunting shot.
As for your Swede, I made match ammo for mine using RL22 and RL25, very slow powders. The all went bang with standard primers. But I was shooting in warm weather.
Anyone using slow powders in 308, 3006, 243, 6.5x55, etc. would be wise to buy a few bricks of Winchester standard primers. This is what Winchester use in their ammo, and they used to use ball power for most offerings.
I tested primers in the dark, so I could see the difference:
CCI Large Rifle
Wolf Large Rifle
Winchester Magnum Rifle