I’d suggest behavior goes both ways.
As of right now casters are often just as tanky as the martials. A stereotypical wizards can have 8 hp, 16 AC with mage armor, a shield spell and use either sleep or magic missile to take out whatever is in front of him. Or if the wizard multiclasses he can match or surpass most fighters AC (most fighters don’t use shields).
In short, outside a few hp - which defensive and control spells easily make up for - the wizard can easily be just as tanky as the fighter - if not more so depending on specific builds of each. So mechanically why would a fighter want to try and defend the wizard? Maybe to help keep a concentration spell going? Other than that he wouldn’t, just kill the enemies as the wizard is just as tanky as him.
IMO, If wizards were actually squishy, fighters would be built to defend them.
Which is my point- if you make Wizards squishy, you have to build Fighters to defend them. But it really feels like most players don't want to defend anyone, they just want to swing big weapons and do big damage, lol.
I only have anecdotal evidence for this; maybe what's happening at most tables is that enemies just attack the Fighters no matter what they do- maybe it's because they do tons of damage, maybe it's part of a social contract or gentleman's agreement, maybe it's just because that's how things have always been done, maybe it's because the DM is tired of hearing "Shield! Silvery Barbs!"...I dunno.
I just know that good tanking options exist, but since people have a choice between those and the ability to deal more damage and we know that Champions are way more popular than Cavaliers, it sure seems like the player base has chosen.
Or maybe in their game Protection Fighting Style is enough, even though it's 1/turn, I really don't know, because I don't have the data.
But I still think it's telling that something I think would be a baseline Defender ability, like say, "any creature within 5 feet of you that's hostile to you has disadvantage on attack rolls against targets other than you or another character with this feature. An enemy is immune to this effect if it can't see or hear you or if it can't be frightened", is not only one choice out of several, it inexplicably isn't available until 14th level, lol.