I've been playing on Xbox since closed beta in May and, look, every multiplayer game is going to have quitters, griefers, etc. It is particularly problematic when the game in question has a small number of players per team (3-5, in Smite's case) and each teammate needs to contribute in order for the team as a whole to win (usually). It happens in Smite, it happens in Halo, in Battlefield, Rocket League -- if it is a multiplayer game, it will have quitters. Some people are just douchebags, you know?
That said, I've never gotten the impression that quitters are more frequent in Smite than any other multiplayer game. If it seems that way to you, it might just be because PS4 is in Alpha and the vast majority of the players are not only new to Smite, but are new to MOBAs in general. A lot of them will jump into a game while only having done the basic tutorial -- if that -- and be completely lost. They'll die a lot, their teammates might not be any better or experienced, so they'll lose a lot. They'll run around with no clue what to do. And since it is a new game in the alpha stage, it is easy for them to think, "Eh, fuck it, I'll just quit and do something else."
That said, the more you play, the less frequent this should become. Whether you're playing in casual or ranked, there is a matchmaking algorithm working behind the scenes in Smite. So the longer you have played and the better you get, the better competition you will be matched up with and against. If you've played for two months consistently, you'll be matched with other people who have played roughly the same amount of time, so on and so forth. As such, you'll be matched with people who at least have a basic grasp on the game and have at least a rough idea of what to do and will thus be less likely to quit just because they are dying and have no idea why, or are running around the entire map just trying to fight players even at level 1 without realizing that's not really how the game works.
As it is now, Smite has barely been available on PS4, so right now you're going to almost always be dealing with brand new, inexperienced players who have no actual idea what this game even is. As such, they have no "stake" in the game or (as they see it) any reason to stick around and suffer through a round in which they are dying a lot and losing. This will be especially noticeable if in a given game, someone has clearly been playing Smite for a long time either on Xbox or PC. I remember in the early days of the Xbox beta, every now and then a player would be on one team who was clearly either a PC transfer or a person who has been playing on PC for a long time and wanted to come enjoy the noob slaughter on Xbox. These people could absolutely clear entire lobbies just by dominating early in Arena or Siege in particular, discouraging new players from even sticking through to the 10:00 mark for a surrender.
Just stick it out. You'll have to deal with people coming and going who just want to check out Smite and will drop it as soon as they realize it is not a game they can fully learn in a few short minutes. The more you play and the longer the game is out on PS4, the less common this will be. :)