Mental exercise: what if a Wizard was built like a fighter?

Have you ever tried to imagine how a wizard would be like if it was built with the design choices of a fighter, without spell slots and cantrips and instead class features that cover the several spells?

For instance, it would have proficiency in every focus, instead of weapon, and every focus would be able to male a spell attack, eg

Staff (two-handed, heavy) 2d6+INT force damage in 5ft

Rod 1d10 + INT lightning in 5ft

Wand 1d6 + INT ranged 60/120 ft

The it would get class features such as Burning Hands, INT times a day you can deal XdX fire damage in a x feet cone

At level 5 you would get extra-cast and be able to attack twice with your focus

If you want access to Fireball, that's a subclass feature of the Evoker only.

Whenever they wanted to release a new spell, it would be part of a new Wizard subclass.

But hey, maybe your DM is dropping you a rare Rod that can use charges to cast Ligthning bolt or something!

This is just a small mental experiment. I'm considering making the whole class as homebrew if I've got time to kill, but the whole point is that I think it illustrates the inherent martial-caster divide effectively.