When you talk about the modern 'shootists', you are painting a pretty broad stroke with one brush.
Which shootists -- the fantastic demonstration shooters who split cards, the ones who hand-throw 7 clay pigeons and nail each one individually before it hits the ground with a pump 12ga? Or the competition shooters, the USPSA/IPSC competitors who run and gun with such rapid-fire precision that even their misses score better than most of us? Or the armed forces/law enforcement precision marksmen -- even within that general class, there are distinctions between the military field marksmen and the law enforcement urban marksmen who have very similar training, but bring different skill sets alongside their shooting.
In any case, I think what you'll find is that in most cases, the shootists might favor a specific weapon, but they are stunningly proficient with just about anything you put in their hand just out of the sheer volume of practice they have had, and their commitment to developing their skills; as the saying goes, it's the archer, not the arrow.
But for the average Range Bubba, accumulating that amount of practice isn't sponsored, routine, dedicated, or in most cases possible with even one gun, let alone each one in the stable. So with the idea that sending rounds downrange is the key to becoming proficient, when Range Bubba dilutes his or her practice by investing range time in multiple guns, rather than building up skill on just one, it has to have a negative impact on proficiency with that one primary weapon.
That being said, just as dry-firing isn't really shooting but helps build skill by developing shooting principles, shooting that classic C96 Mauser does help build proficiency with shooting skills that transfer to enhance proficiency with that 605 that can usually be found riding in the IWB, but not as quickly as investing the time shooting the 605.