CodeFlayer
Explorer
I cast "Detect Light of Gas" 

Arcane Recovery is NOT lame. It just needs a little boost.FINALLY, SOMEONE SAID IT.
I know you're not looking for house rules, and that you have asked for Wizards of the Coast to directly fix this problematic character class. But since that is unlikely to happen soon, I thought I would offer my house-rule for the wizard class that really, truly addresses the problems you listed.
And there you have it! My house-rule for fixing the wizard class. I admit, it takes a bit of elbow grease, but at least it will make the wizard worth playing again. Hopefully Wizards of the Coast will read this post and take action.
- First, you're right about the Hit Dice. Scrap it and boost it up to d10...it won't be as good as the barbarian, but it'll still be pretty good.
- Intelligence is a useless stat, so swap out the wizard's Intelligence save throw for Strength. And while Wisdom is nice, Constitution is nicer...so get rid of that Wisdom save proficiency and get Constitution instead. Now you don't have to ever worry about poison and disease ever again.
- To address the lack of defensive options that you describe (and I agree completely), give the wizard proficiency with light, medium, and heavy armor. And the shield spell is nice, but an actual shield won't use a spell slot...so I give my wizards proficiency with shields too.
- Arcane Recovery is just a silly ability no matter how you look at it. I find that I get more mileage out of the Second Wind ability instead...hit points are really the wizard's major shortcoming, and this really helps reset the balance. So I swap out Second Wind for the lame Arcane Recovery.
- The subclass features are incredibly sad. Who wants to be a scholar? This is a game about hitting things until they die, unless those things are my wizard. Now this is probably the most controversial change of the whole class, and a lot of people are going to balk at it...but I eliminate the whole Arcane Tradition thing, and replace it with the Fighter's subclass options. Before you protest, think about it: Eldritch Knight is clearly a wizard, Battle Master is clearly a wizard with a different 'power source', and who could be more of a Champion than Gandalf? This might be a bit OP for a wizard, though, so I only let it become available at 3rd level (instead of 2nd).
- If you feel your wizard lacks versatility and power after removing the Arcane Tradition, you can add in extra Ability Score Improvements to compensate. My players usually end up selecting feats instead of ability score bonuses, and the right combination of feats can really add a layer of versatility and flexibility. I let my wizards choose ASIs at 4th, 6th, 8th, 12th, 14th, 16th, and 19th levels.
- There's really no fixing the spell slot acquisition problem. The most effective way I've found is to just eliminate the spell slots altogether, cantrips and all, and replace them with weapon proficiencies (all of them). Then I add the Action Surge ability at 3rd level, along with the Extra Attack ability at 5th and 11th level, to help those weapon attacks scale with level (the way the so-called-wizard's cantrips are supposed to.) It really gets back to the heart of the wizard class, which is stabbing things until they die.
- An unfortunate consequence of reworking the spell slots is that you will end up with a lack of defensive magic (notably Counterspell and Dispel Magic). A good way to compensate for that is to add the Indomitable ability at 9th level, 13th level, and 17th level. It will let you reroll a save throw, which is basically cheating but the rules let you get away with it.
- The skill list for wizards, as-written, is too niche and obscure to really be useful on the battlefield. And the battlefield is really where any action is! So drop all of the Intelligence-based skills (Arcana, History, Investigation, Medicine, and Religion) and replace them with skills that will actually be used once in a while: Acrobatics, Animal Handling, Athletics, Intimidation, Perception, and Survival.)
I know right? I'm lurking in those treads, thinking of my Hexblade warlock, and the only thing that comes to mind isI love this thread
it makes an amusing counterpart to the completely serious "Casters vs Martials: Part 1 - Magic, its most basic components" thread