He can easily craft his spell list to be wizardly+. With the massive known list bards get having a spell book and preparing isn't much of an advantage.
Bards are stuck with the spells they know (except for being able to exchange a single spell each time they level). Wizards can prepare different spells each and every day. That is a big advantage for the wizard in versatility. Bards learn 22 spells by level 20. A 20th level wizard can prepare 27 spells at a time, including his signature spells. Even if a wizard chooses to stick with the same spells every day, the wizard still ends up having 5 more spells at his disposal than the bard. The ability to change your spell selection is also an advantage. With the right spells and some good planning, a wizard can adapt to almost any challenge.
And they get access to spells a wizard never will.
The opposite is also true. In fact, the wizard spell list is the largest in the game, dwarfing the bard spell list in size. Bards can cherry pick a few spells with magical secrets, but wizards can still end up having a much larger total selection of spells than bards, and that gap will only continue to widen with every new book that introduces more spells to the game.
Want to summon things in one action instead of one minute boom take the Druid spell.
That's true, though wizards can do similar things with spells like Bigby's hand, animate objects, etc. Not every wizard (or bard) wants to be a summoner, though.
Wizards other gimmick is lore and intelligence but the bard can beat them in that easily since they can get double proficiency bonuses. There are a couple wizard specialties that add something valuable to their spell casting but overall a bard matches them there and maybe trumps them as they can throw in a few out of class spells. But all the non spellcasting stuff you might envision about your wizard. A bard will do it better. So overall IMO if you have a image of a wizard in your head play a bard.
Okay, you have a point there. I do wonder why they didn't give wizards expertise with arcana. I think it's really odd that lore bards and knowledge clerics can be better at arcana than wizards. Still, wizards are usually going to have a higher Int score than bards do, so their total bonus will usually end up being within a couple of points of a bard's for those skills.
Wizards are also among the best ritual casters in the game, second only to tome warlocks. If a bard wants to be able to cast a ritual, he has to know the spell, and it counts against his limited number of spells known (which is already a smaller number than the number of spells a wizard can prepare). Wizards, on the other hand, can learn every ritual spell on their list, and more importantly, they can cast them without preparing them, so they don't count against the number of spells they have available to cast. That gives the wizard a tremendous edge in out-of-combat flexibility that bards can only match at the very high cost of a feat.
There's also arcane recovery, which gives wizards some extra spells per day.
Wizards also get some really nice subclass features that make them better at their chosen school of magic. Wizards can do things like cast fireballs without harming their allies, conjure objects at will, animate stronger and larger undead armies, or get free twin spell with enchantments. Bards can't do any of those things.
I don't think bards are better spellcasters than wizards are. They're a great class, and they can certainly fulfill the role of arcane caster in a party, but they don't make wizards obsolete.