I disagree. 5e RAW a 1 on an attack roll is a miss. That's it. A 1 on an ability check has no particular significance; if you succeed with modifies, you succeed, if not, you fail.
For as many dice as you roll in a combat, 1's will happen (5% of the time to be precise) , it would get really tiresome to have a significant negative impact for each roll (losing hit points, having to replace a piece of equipment, getting attacked an additional time...) every 20th roll. An automatic miss, regardless of modifiers, is enough.
Maybe if we were rolling percentile dice (d100) than a 1 or a 100 should be a bigger deal. Or maybe on a natural 1 during combat you roll a second d20 to see if something bad happens. But not every time.
I lose track of how many time I see 'critical miss' flash on the screen. It seems like more than 5%, and a lot more often than 'critical hit,' but I don't have numbers to prove that, so it could just be an observational bias.
So much this. Any reasonable critical fail table have you at least roll to confirm a critical miss. 5% is a lot.