Many, many years ago, I started reloading with a Lee Loader - it used a punch thing to tap out the primers - set the case on a collar to do that - I still use that part to pop out crimped-in primers - I made a hole through my reloading bench so the primers fall through into a garbage bucket underneath. I do know some people do not bother about cleaning primer pockets - not sure some progressive type systems even have provision for that - and I can not say that cleaned or not cleaned primer pockets have made a difference for me on targets - so perhaps some stubbornness or something coming through with me - I do pop out the primers before tumbling, so that most of the spent primer crap gets cleaned out of there before seating a new primer. But if you are using a walnut shell tumble - you will get granules of walnut stuck in that firing pin hole - so is good idea to check each brass for that, before installing a fresh primer. Likely is why I got into habit to place processed brass mouth down in a loading block - to be able to see the flash holes - and I grab them one-by-one to seat a new primer ...
I know is typical on many presses - certainly the couple of RCBS that I have had - your case gets de-primed on the "up" stroke of the ram, and with a press mounted priming system, you can insert a fresh primer on that "down" stroke - so nothing done there about cleaning out that primer pocket at all.
I do know that using a hand tool like various that are / were sold - Lee, RCBS, Lyman - to clean crap from primer pockets one-by-one, gets "old" really fast - so I prefer not to do that by hand any more. I do also own a "primer pocket uniformer" that is alleged to cut the primer pockets to proper depth - once again, not sure my rifles or my shooting can demonstrate a difference on targets to do that or not - maybe others can show an improvement with theirs - so it has been years since I used it.
Over time, I got both RCBS Large "Heavy Duty" and Small Universal De-cap dies - so in my press they will punch out the primer without touching the outer case wall - the idea for me is to tumble to get rid of crud that might scratch inside of the sizing or bullet seating die - likely could accomplish what I want by just swishing a batch of brass in pail of water with some Dawn and Lemi-shine powder. I sold my walnut hull vibrating tumbler and now use a stainless steel tumbler to wet tumble - again, is stubbornness - to make the cases sparkly shiny, which I am not sure improves groups on target, over just being "clean".
Also - an observation - you say you are going to use a Lee Loader - as I recall, they will only neck size the casing - which some see as a good thing - meaning, however, that any brass that was previously fired in a different chamber than yours, may not fit into your chamber after neck sizing only. Some lever action, pump action and semi-auto do not have very much for camming force - so they often benefit from Small Base resizing. Welcome to the "rabbit hole".