So, I've been playing a human wizard (diviner) in my DM's homebrew setting. Thus far, we've been having a lot of fun with 5e, but I'm growing a bit concerned as we level up and I become more familiar with the rules and spells. I'm honestly at a lose as to what wizards are good for.
Seeing as how you're playing a diviner, maybe they are good at scouting and finding out information?
In past editions, I've played the "god" wizard; battlefield control, debuffs, as well as a support role. I tend to avoid direct damage unless absolutely required; it's a play style I very much enjoy, but I've found it to be difficult to do in this edition of the game. As I've studied the spell section, I've noticed that most of the classics have been altered or nerfed to the point of being fairly pointless; many of the save or suck spells allow a new save each round, and every time I've used them, the opponents either make their initial saving throw, or the next one after being effected for that first round. It's kind of irritating to have my precious few spell slots wasted after a single round.
All of the other classes are quite happy that there are no "god" wizards anymore. My entire group breathed a sigh of relief when they saw how much the wizard had been nerfed. It was never fun to have one character that outshined all the others in nearly every way. But pointless? I fail to see any of the spells as "pointless". Can you give specifics? And no, saying that they make their initial saving throw doesn't mean much except possibly bad luck. As an example, a level 5 wizard casting Web on an ogre would have a 15 DC. This means the ogre has to roll a 15 or higher in order to save against the initial, and then an 11 or higher to save after that, or less than a 50% chance. Or, you could look at a higher level creature, like say, a Dao, where you should be level 11 or so to fight it. You'll have a 17 DC at that level, which means a Dao would have to roll a 16 or higher to save against it, and then an 11 or higher after that to break out. In no other system has web been so viable for so many levels, and that's truly where the Wizard shines. Even at low levels, his spells remain relatively powerful, and they all have some use.
Due to the concentration rule, I can't really augment my teammates anymore. Only having one buff available at a time makes since to counter all the buff stacking back in past editions, but now it feels like it has swung too far in the other direction.
This was a design choice on the developers part, and for good reason. There were way too many times my party would stand outside the big bad's lair, let the wizard put a crazy amount of buffs on them, and then have the group stroll in and massacre what should have been a difficult fight. I'm extremely glad of this change, and it makes the casters still be useful (since spells like haste still exist) without being completely broken.
And then there's direct damage, which has also taken a hit. The damage spells start out strong, but over time are less effective then their past edition counter parts; since you need to use higher level slots to augment them, and you stop getting more than one per spell level past 5th, over time you have weaker fireballs and the like.
Tell me, what edition lets you have a cantrip that does 4d10 points of damage? You also get 2 6th and 7th level spells so I'm not sure where you're getting that you only get one spell. The weird thing is, on these boards, I've almost always seen complaints about how the wizard is too powerful now because his spells do so much damage. Meteor Swarm now does 40d6, fireball adds an extra 2d6 over other editions, and the power words are simply ridiculous.
So now I'm sort of frustrated with my character; all of his options kind of stink now. He's not good at battlefield control, debuffs will be shrugged off, buffs only affect one person in the group, and damage is less than it used to be. Am I missing something, or is magic pointless in the edition?
Overall, I'm enjoying myself. I like this version of the game a lot. But with magic being the way it is now, should I just scrap my character and role a new one?
Not at all. The problem I seem to be getting through reading your post is that you don't like how they've been nerfed across editions, not that they've been nerfed within 5th edition. Go back and compare all of the spells and wizard abilities not to Pathfinder or 3.5, but to the other characters in the game. I think you'll find that they compare very favorably. And remember, combat is only one part of the equation. Wizards are good in all three pillars, which is something not a lot of classes can say.