Small primer could put more force on the primer though and if youre shooting a rifle with a large firing pin that additional force may be enough to pop the primer.
So if you have a sloppy factory action then the small primer brass might not be a good match.
The size of the firing isn't the issue. It's the size of the FP hole in the bolt face, in relation to the FP itself. Like Greg talks about in the 1st of his video. It's a matter of the primer cup being allowed to flow backward thru the gap. Cratering usually happens at 1st. Then as time goes by, the hole smooths out (widens a tad) allowing the crater to become a pierced. Of course we all know, it doesn't take many blanked primers and you've roached the bolt face with hot gases.
Small FP's (.062" +/-), , Large (.073" +/-). I like to see a difference of no more than .002" between the FP and the FP hole, regardless if it's large or small FP. I've had RPR's, Remmy's, Sav's and Thompsons all come thru my shop with some blanking SP's and others not. I've seen RPR's with as much as .010" difference in pin to hole size. It, of course, blanked SP's, regardless of primer brand. That particular rifle was even blanking factory loads, with LP's.
I done tests back in the middle 90's with a ton BR rifles that required bushing the bolt to prevent blanking. There is a direct relation between headspace and FP spring weight, too. Back then, there were some running inert (at rest) FP springs. Nowadays, everyone is running cock on close (striker type). Since most bump their shoulder back .002". The case jumps forward when the FP hits, before it is pushed back. With inert FP's, the spring has already withdrawn the pin before this happens, allowing the primer cup to flow quicker. Cock on close (sticker) types don't have the spring tension rearward, allowing the FP to stay in contact with the indentation longer, preventing it from flowing as readily. A long headspaced chamber gives the case a much father 'stopping' point before it is force rearward. Which can allow for the FP to already start its withdraw sooner. Blanked primers are more noticeable in long HS's chambers when using factory loads or when FL sizing back to saami specs.
Not really sure what you're referring to when you say "...sloppy action..." If you mean not locking up tight. Maybe. But, would lean towards my headspace comments, too.
Sorry for the ramble. To the OP:
SP pockets tend not to 'loosen up' as quickly as LP.
