When I first wrote the piece about heraldry, it was largely off the series finale of Game of Thrones, and thinking about the banners which were a signature of the show. But I did some research on the most common sports team name/mascots, and came up with some interesting results.
It should be no surprise that eagle is the most popular mascot in all sports, from collegiate to pro. It's always been a popular symbol, from antiquity to American culture itself. Even when it's not specifically the bald eagle, we can imagine it being a frequent standard. "Falcon" and "Hawk" are also very ubiquitous, though some may have difficulty distinguishing.
What's very interesting is that the second most common is "tiger", which, as a non-native animal to the Americas, really is a testament to its popularity. I've said before that the tiger might overwhelm the as a heraldic beast for medieval Americans, due the latter's association with monarchies, which Medieval Americans would spend centuries trying to assure people that they're not coming back. Still, lions are no slouches, as larger cats make up half of the top ten. Panthers are also more popular, and as they are conceivably a New World creature, and a symbolic animal to those of African descent, they make sense as a frequent standard. (In fact, the African panther was fairly popular in Medieval Europe, and according to legend had fragrant breath.) The cougar, the quintessential North American "big cat" is another popular one. What's interesting is "wildcat", which in nature is something of a pre-domesticated cat, not extant in the Americas, but it's quite possibly people pick the name because it sounds a little more intimidating than "Bobcat", which may actually be the standard.
The cardinal is the most common non-predatory bird, and is an exclusive new world animal. Its distinctive look, and low key patriotism would probably appeal to those who want to add it to their coat of arms. In fact, it's one of the most six team names that so common as to belong to two respective of the "big four"sports. The others are aforementioned Panthers, as well as Giants, Kings, Rangers and Jets. Now "Giant" could be an interesting symbol, but as for the others--there are no more "jets", as mentioned before American Warlords don't want to associate themselves with European monarchs if they can help it (And a crown would be a flourish anyways), and the concept of "Ranger" would be too vague. (When Texas refers to "Rangers" and New York refers to "Rangers" they've very different things.
It should be said these six don't count team names which are synonymous. For instance Bengals/Tigers, Bears/Bruins, the various names for horses, and then of course, the countless names, some of them fairly derogatory, in reference to American Indians. For better or for worse, it's very likely Native American imagery would make its way into a lot Medieval American heraldry. They're both "exotic", but at the same time warlords would very frequently claim Indian blood for the sake of propriety. Other human warrior classes might be hard to implement into imagery. Maybe somebody who looks like a soldier of Classical Antiquity, but the unlearned would not be able to tell if it was meant to be a Trojan or a Spartan. A cowboy might be unlikely, as cowboys are considered antithetical to the knight's class. And of course, a knight might come across as absurdly redundant for a heraldic symbol, like a tuxedo t-shirt, or wearing a portrait of your own face.