Before typing what I am about to type, I want to state that I am not stating this out of defense or rudeness, merely only out of debate and for the sake of bringing to the table another portion of the argument.
That being said, what it sounds like your telling me is the same with the item system. You can search for AD items, AP items and anything else you want to search for, so then why did they implement a customizable set option. The argument is the same as with the champion selection and everything else Riot has been trying to work for, clarity, and more importantly to reduce visual noise.
My argument for the original post, and why it is more effective, is because it reduces visual clarity. When your looking at all of the champions (which I do own EVERY champion), the visual noise is too much. I go through champ select and overlook some of the fun champions for the roles I am filling because of this noise. Why do I struggle to find my supports out of the rest of the champions, well I have been around long enough that sometimes I forget who I have practiced, or forget who is good in specific situations. Everyone learns differently, and I associate my learning with visual queues, and as such the visual noise does nothing more than become a burden when trying to make decisions in the mere 45 seconds I have to choose.
This is further complicated by trying to find outliers in the current system while trying to make your decision. For example, Thresh, a support-yes, but a tank-no, atleast not according to the system. So when I try to weigh out what tank I want to support as he isn't on the list. Or if I decide I want to play a mage, why doesn't Akali show up on the list. Sure the system is functional, and I am not claiming it is broken, merely claiming that it is not effective for everyone.
The current system, while effective, is still very time consuming, especially considering the fact that you have to manually type in anything you are searching for, like "tank", "assassin", "support" etc. This is compounded with the fact that those who are slow with typing struggle with this, as well as the fact that those who are good at typing will instinctively put a space after their word which resets the search and you have to type it again. I know that the main reason I don't use the search box is because more often than not I waste time because I typed "marksman " instead of "marksman". If they had checkboxes that would be much more effective, much like the website is.
I know most players will see an enemy champ and go "I want to play XXX" but not everyone does, and if you do I envy you, but not all of us have that gift, and we need something to make this simpler for us to make those decisions.
As stated before, this is not typed with the intention of being rude or condescending or in anyway toxic, so please don't take it as such and please, I would love to know what your response is to this.