I very much agree with the core statement here, even if I take some issue with the manner in which it's presented (the OP gives examples of how min-maxing is bad, but then argues that champions shouldn't be overloaded). I very much agree that any champion should not only have clear strengths in weaknesses, but should also have a certain set of things that they categorically lack. I think we need far more champions lacking in mobility or CC, for instance, and I think the rule to follow should be that a champion shouldn't have something unless it's meant to be a core contribution of theirs.
With that in mind, though, being lacking in something is different from not being able to respond to a certain situation. I think every champion should be lacking in certain things, but I also think every champion should also be able to have at least some choice when faced with an adverse situation, even if it's not some perfect counter-answer. One of the reasons why Kalista is so unhealthy to play against whenever she's strong, for example, is because she counters champions lacking in range and mobility so hard that they effectively don't get to play at all when she's around. On the flipside, one of the biggest problems with juggernauts is that many of them can't do anything if the enemy team is even remotely competent at kiting.
This isn't to say that every juggernaut should be given range, mobility or both (in fact, I think they could probably have even less of either), rather, I feel some of their defensive power should be shifted onto features that are appropriate to them, while still giving them more choice overall, such as mechanics that let them resist CC. In the end, they'd still be lacking in range and mobility, but would be able to afford that precisely because they'd have access to stuff others don't. This, imo, is a philosophy that should be extended to all champions, and that should probably be used to cut deep into a lot of overloaded kits.