Should players constantly going past double digit death's be flagged?

no, because this would lead to some stupid as hell bans, like in normals it could be a premade of golds vs a bunch of Lv.10 - 20 players, leading to a stupid ban then.

In ranked games yes... FOR THE LOVE OF GOD YES !

(Edit) The system shouldn't just flag you for deaths. In some games that go long this is not a good thing. SO rationally this system would look at an equation. Deaths x Kill Participation divided by game length to obtain a number that determines if you were int'ing. Or something like that seeing as Riot is a fan of automated equations that work behind the scenes rather than giving us back ther tribunal.

In ranked, yes.

If you're dying more than 10 times in a game then you're obviously doing something wrong and you need more time to practice and are clearly not ready for ranked.

I don't think you should be banned, but I do believe that being restricted to normal games for a period of time until you can lower your average number of deaths would be appropriate.

Mind you, this will NEVER HAPPEN, but it's fun to dream.

Doesn't the LP system already handle this? People constantly dying 10+ times are probably winning lower than 50% of their matches and will be demoted to a more appropriate rank.

Specific punishments for poor performance are dangerous to implement. I can easily imagine junglers camping losing enemies in order to run up the score against them and force a ranked game restriction, or refusing to end a game in order to destroy the enemy's KDA.

It also encourages selfish play to protect one's KDA. As a support main, I'll often sacrifice myself for a carry by taking a skillshot or something of that nature. But if I've lost two games in a row, maybe I don't make the smart play in order to prevent my own KDA from dropping into a danger zone.