LeaverBuster does very little to discourage toxicity and misses the real issue.
The new LeaverBuster system unfairly punishes players for connection issues. This has been acknowledged by Lyte, and apparently Riot (or at least Lyte), is okay with this. I think this is rationalized to be an acceptable trade off for a system that improves the game experience for other players. The problem, however, is that I believe that LeaverBuster does very little to actually improve the game experience of other players, at least in ranked. (I almost never play non-ranked, so I have no idea why people AFK in non-ranked.)
In ranked, in my experience in over 1000+ matches in season 4, there are three reasons a player stops playing early:
(1) The player disconnects/crashes/has connection issues; (2) The player has to go because of real life demands; or (3) The player rage quits / AFKs.
In my experience, (1) is by far the most common by a wide margin. The majority of AFK/disconnects I experienced in season 4 actually involved a player never connecting to the game at all, or disconnecting within the first several levels. Obviously, LeaverBuster does nothing to discourage disconnects, and unfairly punishes those players who disconnect. At least with respect to ranked, it is unnecessary to punish players for disconnects, as the player is already being punished with a loss, and their ranking and win rate already reflects their disconnect rate (more on this later).
With respect to (2), this is in my experience the rarest of the three reasons. This could on occasion take the form of an actual emergency (e.g. a medical emergency), in which case, obviously, LeaverBuster is going to do nothing to discourage players from quitting (at least I would hope it does nothing to discourage quitting in the face of an actual emergency). Much more commonly, however, younger players are simply told by a parent that they have to stop playing for one reason or another. This seems to happen more often than I would have expected, but is still very rare in ranked.
With respect to (3), this would seem to be the category of player that LeaverBuster might be targeted towards, and LeaverBuster could indeed discourage players from rage quitting or AFKing - the problem is that I don't believe that this does much to improve the game experience of players in a game with the potential rage quitter.
In my experience, generally, when a player chooses to AFK or rage quit, it is because he is in a situation that feels hopeless to him. This may be because he is losing lane terribly, or because his entire team is way down, etc. In my experience, most players who get in this situation and who are prone to rage quit are frustrated either because (i) they don't understand the game well enough to understand why they are losing or how to get back in the game, or because (ii) they feel their team has no chance of winning. In either event, these players almost invariably have something else in common: they aren't emotionally/intellectually mature enough to handle a bad situation in a constructive way.
In analyzing the impact of LeaverBuster, then, we are looking at players who would, sans LeaverBuster, rage quit or AFK, but who are discouraged from doing so by LeaverBuster. So how will these players act in such a situation? There are plenty of examples of how they will act: exactly the same as players in the current system who rage but are discouraged from leaving by the current timeout / ban system.
And how do these players react? As soon as they believe the game is lost, they stop trying to win and start trying to find someone on their team to blame for the loss. They start blaming the jungle, or a laner with a negative score, or the ADC, or anyone but them self basically. They might start intentionally feeding. They might start farming the jungle and ignoring objectives. They might spend the entire game typing about how bad everyone else is. Regardless of what they choose to do, your chances of winning with this player "playing" is only marginally higher than if they AFKed. Sure, it's higher, but given that players who want to AFK are generally behind, don't understand the game that well, and aren't willing to listen, I'm not sure that your game experience is that much improved just by discouraging the player from AFKing
The real issue is that you run into players like this ALL THE TIME in lower ELO ranked. You also run into mature, friendly, cooperative players who rarely feed and do everything they can to help the team win. The frustrating part is that these players are at the same ELO and are stuck playing in the same games.
Having a player in your game AFK or disconnect happens occasionally, and is sometimes frustrating, but it doesn't happen often enough that it really impacts your ability to win games and climb the ladder, and in fact if you never have any connection issues it helps you as it happens more often to players on the enemy team (5 enemies = 5 chances to disconnect, 4 team mates = 4 chances to disconnect).
On the other hand, having a player in your game feed and become toxic happens every other game at low ELOs.
So why does this matter. As long as you don't feed, shouldn't that make it easier to win? If there are five enemies and only four team mates then shouldn't that mean that as long as you aren't feeding you will win more often than you lose? Unfortunately, this isn't true at all for several reasons.
I really don't want to turn this into a discussion of the ranked system, because I understand why it is the way that it is, but the reality is that right now it does a terrible job of ranking players. In a tautological way you can say that you are where you deserve, but the reality is that this misses the point that many players in gold would struggle to get back there if placed in bronze, while many players in bronze would do fine in gold. The skill set needed to climb out of bronze is completely different from the teamwork ideal LoL espouses. Watch any popular streamer and their advice for climbing out of bronze will basically amount to: play a hard carry champion and ignore your team mates. They specifically advise against playing a tank or support champion, and generally never recommend playing ADC either. You repeatedly see comments that you are going to be very frustrated if you try to play anything but mid or jungle, and if you try to play anything but a hard carry with high damage and mobility.
I can't believe that this is your intention. This might seem like I've gone far afield, but I mention it because the reason that hard carry champions are recommended for bronze/silver is the same reason that people rage quit so often at lower ELOs: many players in lower ELO have no idea how to play once behind, and will feed so badly the game will be out of reach. High burst, snowball champions are strong at low ELO because they can take advantage of this. Team oriented champions are bad because they can't take advantage of this as much.
I have no idea what the solution is, but THIS is what is ruining people's game experience, not quitting / AFKing. Quitting / AFKing isn't actually the real issue that is ruining player's game experience - instead it is only a symptom of the real problem. LeaverBuster does nothing to address the real issue - it just addresses one of the symptoms. Unfortunately, in doing so, it unfairly punishes those with connection issues. This would maybe be an acceptable trade-off if it had a big impact on curbing toxicity, but if it is just addressing a symptom and doing nothing to address what is really causing negative game experiences, it doesn't seem worth it.