If you are frustrated that people around you are irresponsible, you should try giving them responsibility for something important. Give it to them with the trust that they will see it through and full freedom to solve the problem. See what happens.
Maybe they will surprise you with an approach you hadn't considered. Be sure to leave room for yourself to be persuaded if their way will achieve the goal. It's important not to be prescriptive about specific solutions.
Assess any solution in terms of characteristics and requirements. Is it reliable? Is it succint? Is it easy or hard to deploy? Can we tell if everything is configured correctly?
By talking about requirements and characteristics, we can avoid prescribing specific solutions. This gives the person leading a task more creative control.
You're probably thinking that it's a good idea to define what these are before handing a task out. I agree.
One possible outcome is that the person will prove that they are not to be trusted with responsibility. I don't actually think this is very likely if they really have creative control. I find that when I actually take the time to talk to people, that they seem much more thoughtful than I would have guessed. I suppose that's a good reason to talk to people more often.
There are things that look like irresponsibility on the outside that are other things when you look under the hood. Maybe they are busy and have bitten off more than they can handle for a time. Maybe you have clarity on something because you have developed a way of thinking about it but you haven't shared this with anyone else. Be open to what you hear and don't always demand to understand why.
To see people in their glory, entrust people with things that are important. There will be things that are so important that you feel tempted to do it yourself rather than entrusting them to someone else. But if you ask another person to take up a task and help the other person to see that it is important, you may observe a level of engagement from them that you haven't seen in the past. It's possible that the people who seem irresponsible and apathetic are the ones who care the most but don't feel like they have something worth caring about to do.
Don't judge them for not having found the right place to apply themselves. Maybe that's your role on the team: to expose opportunities for people to lead.
This is an experiment. Think of it as a long term one.
The easiest way to feel impoverished and bored with life is to think that you have everything and everyone figured out. It doesn't take much to dispel yourself of this notion. You just need to let yourself start seeing again.
See people as they are and see them for their potentials too. And let them surprise you as they surprise themselves. You may find that the extent to which people have themselves figured out is less than you had guessed. And if you see that, it will be easier to think of the game you are playing as more similar to Golf than Tennis. It isn't one-on-one with a winner and a loser.
It's each person trying to do meaningful work just a bit better each time we do it. It's just us learning and growing and practicing... always.