The fundamental problem with the new champion select is the designers, as well as many players, didn't really understand the purpose of fill in the old champion select.
In the old champion select, there were often struggles between the players over particular roles and the purpose of saying fill was so that you didn't end up in an argument with another player wanting the same role. When the new champion select came out, that problem by and large went away and with it the concept of filling also went away.
In the new champion select, fill has come to mean that you want to play the least desired role. And that is the fundamental problem with the new champion select. Who wants to play the least desired role in the game? The answer is: very few players want to. That is why it is the least desired role!
Ok, but what's the real problem with redefining what it means to fill? Why not have fill mean to choose the least desired role?
The problem is that most players will play the least desired role in the game if they have to. So by giving players the option to categorically not play certain roles, the system increases the shortage of players for those roles. Moreover, players will queue for popular roles not because they want to play the most popular roles, but because it increases their chances of getting the roles they really want to play. This all amounts to the system having trouble accurately matching players with their desired roles.
The solution is to force all players to have a small chance of playing every role in the game when they queue. This may seem like a very unpopular idea for players, because players don't want to play the least desired roles in the game! But, if every player has a slight chance to play any role in the game, then the overall chance a player can get matched into their most desired roles will increase because there won't be as absurd of a demand for players in the least desired roles!
It has been suggested that for players that desire to play all the roles equally, that they randomize picking primary secondary using six-sided dice at home. That this is considered a solution just makes the problem with the new champion select so much more obvious! Unless you use a weighted die players using a d6 probably won't realize their dreams of playing all the roles equally, but good luck anyways!