The new system works well for ranked gameplay, because that's what it was built for. To still have the draft pick integrated, but add Team Builder-esque elements with selecting champions and roles. But for normal queue it makes no sense when compared to Team Builder and actually does a worse job.
Team Builder was perfect, not to mention it worked. You select your champion, then the role you were to fill with that champion. You were guaranteed the champion and role. There is no "searching through your match history for what a computer thinks is the best suited role for you." (which to be honest I've not heard of this being the basis for determining which role you'll get, but if so this system is that much worse than I thought) Majority of the time, matchmaking does not give me the role I wish to play, even set as primary. I also don't understand why the secondary role is a requirement in the first place. What if I only want to play one role at any given time (usually my case)? I'm screwed based on what the game believes I'm good at (apparently), or chance. I can imagine why the secondary role is there, but it should be optional. I don't understand why the game would match two players who have the same primary role in the first place. This is a major fault with the system, it simply doesn't make sense.
For example, I like to play jungle, so I set it as my primary. Support as my secondary, as it is my next best role. Majority of the time I will end up playing support. I've been told it's because it's an unpopular role that is easily filled regardless of the selected primary. Okay, so I select mid. Same results. I do not buy into the "solution" to this fault being "select a popular role!" It is not a solution whatsoever. It is a fault, and it needs to be fixed. Why can't I select the role I want to play, then have the game match me with players who fill other roles? Because Team Builder was removed from the client.
One other theory I have that we'll have to see about when Jhin comes out, is how new champions will work in this new system. Anyone that's played ranked when a new champ is released knows they are banned almost every game. With this new draft mode, I imagine it will be no different. That said, besides blind pick (which won't work well either with insta-lockers), will no one even be able to try new champions? They'll either be banned every game because people don't know how to play with or against that new champion. Let's say you manage to lock in that champion, other players can still dodge. Chances you might be able to play a new champion you were eager for are severely cut, already due to people dodging, but now bans will play a role in this as well. Maybe it's a bit unrealistic to think about, but it's still a possibility.
This new system is flawed for any player that is looking to play the game non-competitively in normal matches. Having a computer deciding which roles are best for you does not make good system by any means. Computers are some of the dumbest machines in existence, how can you expect them to make decisions better than a human? Really, in most debates I've heard between "New Draft" & Team Builder is that Team Builder took too long to find a game because the lack of role x or y. At least in Team Builder I could play which role I wanted, guaranteed.
Also, "honestly people should stop complaining, if u have problems just go work at riot geez." This makes no sense. Absolutely no sense. I have complaints because I see clear flaws in the system. Flaws the majority of the community does not see for some reason. That or they're silent about it. Or I'm completely missing something others see working fine. I can't even address the ladder part of that comment, just.. what do you even mean?
TL;DR - New Draft is flawed based on primary and secondary role selection and needs to be fixed, or Team Builder needs to be reintroduced as a different game option.