There's no right answer to whether someone should train quads. That depends on the individual skater. I think for skaters like the 3A currently, who have consistent and big triples, a quad is the next step. It's like if you have all your doubles and they have the height/distance/rotation potential for a triple, then you go onto a triple. And we can't even discuss quads overall, as each skaters have stronger and weaker jumps; for some it's easier to do a quad than a different triple.
For example, Liza recently got a 4T and has been doing 3As very consistently, yet she didn't even jump a 3S this season. Anna and Sasha both have quads, but haven't landed a 3A yet. Alena got her 3A before any quads because the 2A was her strongest jump. I think training a 4T is a good step to take; her -3T looks as easy for her as some others' -2Ts. Based on how that jump looks, I don't think she'd be more prone to injury training a 4T than a skater who is trying to go from a 2T to a 3T. Alena's salchow is another one of her strongest jumps, so I see a potential for a 4S too.
On the other hand, I don't think we're ever going to see a 4S from Liza or Anna, or a 4Lo from Alena as those are their weak jumps. It all depends on the individual skater, there's not blanket answer for all skaters.
As for learning quads just for winning, that's impossible to predict. The judges decide who wins and you can't control how others skate or what jumps they will learn. Maybe Alena wants a quad just for herself? If she wants to, is ready for it technically, and can do so in an environment monitored by professionals, she should go for it. Sasha has the right idea - not everything is about winning (and it's not in your control) but if you just learn what you want to (safely) and show what you can do, that will be your passion and motivation. Afterall, when Sasha learned her first quad no one else was doing them and she certainly didn't need them to win. I think that's a far better mindset than just wanting to win, because that's really out of your hands. This goes for not just jumps, but spins, SS, choreography, etc. Everyone has their own favourite elements in the sport.