Is there a downside to tenderizing meat?
Almost any cut of meat can be pounded--very thin steaks commonly called cutlets or scallopini are made from tender cuts being pounded thin.   This is most often done with chicken or pork, but you will also find, for example, medallions of beef tenderloin pounded to get them into a uniform shape and size.  

Obviously, this is work to do, and changes the shape (and thus the cooking properties) of the cut involved, but does not really have a negative effect.



Your butcher did not pound the meat. Instead, he ran it through a commercial version of a jacquard meat tenderizer.  The home version looks like this, with many small pointy blades or needles to penetrate the meat:


Picture from Chef's Catalog

They are used to create many, many small cuts in the meat, physically severing the connective tissue and making it more tender.   The most frequent home use is to make cube steakl; they are also often employed in making chicken fried steak.

The many small holes may also help the steak absorb some seasoning from a marinade.



Is there a guide to which types of meat work better with which types of tenderization? 

Tender cuts like chicken breasts, beef filet, pork loin, and so on don't need any tenderization.  THey may be pounded to reshape them, but there is no real requirement.

Tough cuts, typically beef, may be physically pounded or subjected to the tender mercies of the jacquard tenderizer in order to render them easier to eat and more succulent when they are being used for a rapid cooking method like chicken fried steak.  If they are being used in a low and slow method, like braising or barbecuing, there is no point and the many small holes would be a detriment as they would allow more moisture to be expressed.

Can you over-pound or over-slice a cut of meat and damage it or cause it to toughen?

Yes, eventually you will reduce it to shreds, or make to thin and unattractive.

Does manual tenderizing conflict with other types of tenderization (e.g. brasing, enzymatic, brining, marinating etc.)?

Firstly, neither brining nor marinating tenderize, ever, unless there is acid or an active enzymatic ingredient in the marinade to do it.

Braising (and other low and slow methods) work by converting the connective tissue protein collagen into gelatin, thus making the cut succulent and tender, despite being very well done.  IF you are going to do this, there simply is no point in mechanical tenderization.

Enzymatic tenderization works by denaturing the proteins in the meat, and if over done will turn them to mush.   It also works only at the surface, unless left long enough to penetrate--but then the surface will mushy.   Using a jacquard might be helpful in getting an enzymatic marindate to penetrate and act on some of the interior of the cut, but I personally do not like the outcome from enzymatic treatments, and never use them.