Silliness lies in the eye of the beholder.
In the early silent pictures, you can see a Harold Lloyd character being made fun of for wearing out of date clothes from a few decades back. In the 1960's, young whippersnappers had a whole different style and thought all the previous styles of non-groovy people were square. In the 1970's, mainstream clothes started looking radically different, and by the 1980's, people started thinking the 1970's clothes were ridiculous, and did SO much better with their cool sweatbands, shoulderpads, etc. Those clothes in turn were considered unwearable in the 1990's, and then clothes as seen in the 60's and 70's became retro-cool, etc etc etc.
Your medieval clothing examples suffer a bit for the faces and the unfamiliar jester-like head-stocking and perhaps the choices of colors for the art. Meanwhile, while I personally think the Aragorn picture looks pretty cool (also not particularly ahistorical), I'm not much of a fan of your second example of super-hero-like costumes (they look like impractical modern fantasy costumes to me).
There was quite a range of actual medieval clothing, and I find some of it pretty attractive and would even wear it if it were socially acceptable. It's mainly a matter of what people were used to and knew how to make.
I would have a hard time liking giant codpieces, or some of the more elaborate and uncomfortable-looking clothes, but that's just my own modern and personal tastes, and I don't much care for uncomfortable fancy modern clothes, either. I think high heels are ridiculous things for women to wear and suffer with. But that's fairly irrelevant, and all fashion opinion is subjective rather than fact, except perhaps for observations about practicality of construction and wear for certain occasions.
Medieval clothing for being bad-ass, that is, fighting attire, was mostly very practical, with the possible exceptions of codpiece armor (much of which was thrown away by collectors e.g. during the prudish Elizabethan era), and some of the amazing helmet ornaments used for tournaments.
I'd say a lot of actual medieval fighting clothing both looks as was pretty "bad-ass" (though language style has also changed - see Shakespeare or Homer for how much much cooler their language skills were, including swearing and put-downs).
I'd say another factor in the perception that actual medieval clothing was not bad-ass, also comes from how they had to make it by hand without any modern industrial techniques, and also how when we try to make their clothes, we lack the craft skills they had for making those types of clothes, and we don't spend the same amount of time and attention making them that they would have.
Furthermore, our art for bad-ass fantasy characters like freakin' Aragorn or super-heroes or D&D art, have ridiculously high standards and match modern ideals for personal beauty and excellence, while actual typical people don't look like that (and even many of our super-models don't look like we usually see them, when not helped by Photoshop, editing, teams of professional make-up artists, super-expensive brand new new clothes, etc).
So for a fairer superstar attractiveness comparison, compare Vigo Mortenson as Aragorn to something like this Scottish statue of William Wallace, maybe:
Certainly our real modern people mostly are not so impressive looking.
So "the accepted image of fantasy clothing" perhaps "come[s] from" a combination of cherry-picking historical examples that happen to match our current aesthetics, combined with cherry-picked beautiful people and art and compatible modern elements, to produce images that modern eyes tend to recognize as attractive, one way or another.
I see in comments you are wondering about the modern origin, which I would say you can see developing on sword & sorcery style pulp fiction book covers from the early 20th Century, particularly on Conan (when he wears clothes...) evolving in style:
And of course there were bikinis for women, leading to chainmail bikini phenomenon seen on Red Sonja.
However I think those styles borrowed both from actual historical sources as well as earlier European romantic medieval fantasy art - what comes to mind in particular is from about 1900, and is for its own sake not for pulp fiction covers. I'd say it in turn was inspired by 19th Century romanticism, as seen in Wagnerian opera.
I'd say this 1910 Wagnerian Brunhilde by English illustrator Arthur Rackham would fit in quite well in most modern medieval/fantasy fashion line-ups
And earlier - Europeans have been re-appreciating their medieval and ancient costumes and armor on and off since the Renaissance, re-imagining and combining clothing and armor styles for centuries. I assume these more artistic and historical sources provided inspiration for some of what made its way onto the modern pulp fiction covers, then later covers, then game books, films, etc.
There was also clearly input from all the ancient fantasy fiction and films.
And in the later 20th century, American fantasy armor seemed to get mixed up with American Football armor (huge shoulderpads).