I think it partially depends on what you consider "proficient"
Most hobbiest / collectors are usually capable of using the weapons they own...but many collectors own an astonishing amount of pieces, so true continual mastery may be difficult with the exception of a few of them.
Most solely self-defense or combat oriented users will limit themselves to a particular set of platforms because in their eyes, maximum proficiency with a few tools is more likely to pay off than a large collection of tools.
What each one of these individuals considers "proficient" is undoubtedly very far from the others prospective.
The "professional" prospective, for lack of a better term-, would not consider anything less than full combat capability... CQB, 25, 50, 200, and longer Marksman rating sustained fire
depending on the weapon platform- while executing tactical movements and magazine dumps while communicating with fellow shooters to neutralize multiple threats.
The hobbiest/ collector might consider proficiency the ability to clean and service each piece, and fire it at its intended target multiple times to successful effect. 2-4" groups for pistols beyond 15 yards, 20-23 runs on clays, and 1" groups on hunting rifles with limited magazine capacity. These figures are just an example.
Granted, we all want to be better shooters...but a combination of natural and learned ability, practice ( time and money availability), and weapon capability will limit the hobbiest over the "professional"
There is a little bit of the eternal argument here, thats for sure.
I will say however, that even the collectors with the broadest collections will have one or two items that they both value- and can use- much better than the others. Often times, this pairing results because of the collectors varied interests and pursuit of that perfect piece or pieces that suit them "just so".
Those would be the pieces of ultimate reliability and function to those individuals...and would be kept at the bedside, at the ready on the hunting rack, or squirreled away with packs of ammo for something we all hope never comes.
We all have those
We use them well, and we use them often...which came first can be the chicken and egg argument.
So I would say to your question- No.
Having and using a variety of firearms does not necessarily limit your ability to use those pieces that you use best in your collection, however large that collection may be, in the event that you need them for your own survival. This statement is predicated on the belief that you will regularly use the pieces you deem most important to you as the tools you need them to be.