The phenomenon of impractical superhero costumes is not a new one. Countless comic book characters have had to fight bad guys while wearing the kind of garb that makes it difficult to do any physical activity, and that’s doubly true for the women. It goes without saying that, on occasion, the questionable costuming extends to the appearance of impractical superhero shoes.
The superheroes of Marvel and DC Comics jump, kick, and flip on a daily basis - and some of them do it in footwear that wouldn’t be suitable for walking a mile. High heels, platforms, and booties are all common items in a crimefighter’s shoe closet - right next to the combat boots and running shoes one would normally associate with their line of work. Sometimes, function takes a backseat to fashion - even when you're one of Earth's Mightiest Heroes.
Emma Frost has the unique ability to take the skimpy, male-gaze-intended garb of the stereotypical superheroine and absolutely own it. As one of mutant-kind's resident psychic powerhouses, Frost can get away with her underwear- and corset-heavy wardrobe - and that goes double for her love of thigh-high boots.
However, in Grant Morrison’s New X-Men - right around the time that Emma switches to a more daring platform heel - it's revealed that Frost has a secondary mutation that can turn her skin to diamond at will. This leads to her actually engaging in the martial side of superheroics a lot more than she did in the past. But she still hasn't made the switch to a more comfortable choice of footwear.
DC Comics' New 52 reboot in 2011 brought about new status quos - and new costumes - for all of the heroes and villains in its catalogue. While most of these changes were well-received, others were not - and Kara Zor-El takes a notable loss in the fashion department.
In an effort to get away from her traditional skirted look, the New 52 Supergirl combines a bikini bottom with thigh-high boots that inexplicably fail to cover her knees. Though mobility is the presumptive reason for the cutout section, that doesn’t seem like it should be an issue for someone who spends much of her time flying through the air - nor does it seem like it should necessitate leaving her knees completely exposed. These days, the boots have been quietly retired to the back of Kara's closet.
The costume Bruce Wayne provides for his young ward, Dick Grayson, in 1940’s Detective Comics #38 has a lot of immediate issues with it - and the footwear is definitely one of them, though perhaps not as obvious a problem as the lack of pants. The Batman sends Robin on nighttime missions against the worst Gotham City has to offer in nothing more than pixie booties - which fit loose and don't appear to offer any protection or support.
The Boy Wonder has to fight villains in slippers for the next few hundred issues and several decades - well into his time with the Teen Titans. Robin wears the spritely footwear until he gives up the gig to become Nightwing - and then Jason Todd steps into his booties. It isn't until the emergence of the third Robin, Tim Drake, that the Dark Knight's sidekick starts wearing more reasonable footwear.
Walt Simonson’s epic run on The Mighty Thor - lasting from 1983-1987 - is rightfully recognized as a formative period for the God of Thunder. Thankfully, not all of the fashion cues laid down by Simonson have stuck around. Under his pen, Thor started sporting a set of armored leggings that were wrapped up in an excessive amount of golden bandaging - and that culminated in the sort of kneepads that could only result in chafing and obstruction.
Thor's kneecap protectors are so large that he almost has to be portrayed in a powerful stance with his legs spread apart; if he were to be shown in motion, they'd be clanging against one another. It's not a terribly practical piece of equipment, even for an Asgardian - nor is it something a real Viking would ever even consider.