Interestingly, though, if you make these changes then I'm not sure the game will really have the OD&D feel.
I think that Mearls got that reasonably right in one of the earlier
Legends and Lore columns:
Right from the beginning, we have a nice encapsulation of the relationship between fighters and wizards. Fighters protected wizards, who eventually became the most powerful characters. A sleep spell was often the difference between victory and defeat in the early days. Thus, wizards were carefully protected by fighters and other characters to preserve them for just the right time to take down a whole mess of monsters.
On the face of it, this might seem like a bizarre way to design a game...
In the early days of D&D, and to some extent through 3rd Edition, death was a cruel, capricious mistress...
In this situation, play skill focused more on your ability to come up with a good plan or figure out the clues that pointed to a hidden trap or treasure. Character power was at the whim of the dice, making the concept of building your character largely irrelevant. Aside from choosing class and race, you had few decisions to make. How you played your character, rather than how you built it, determined your chances of success.
Against this backdrop, the disparity between wizards and fighters make sense. The fighter was akin to playing in easy mode. You had more hit points, better AC, and access to weapons. All things being equal, when it came time to use the rules to determine if you lived or died, the fighter had a leg up at low levels...
In some ways, playing a magic-user was like opting for hard mode.
When you think about the game in those terms, the disparity starts to make sense. If you played in easy mode, you had a better chance of survival but a lower ceiling of power. In hard mode, you ran the risk of losing a character in exchange for a shot at accessing powerful spells.
I think you're right that the core 5e game will try and put fighters and wizards on a par. But I wonder if there will be a module which lets you use them in the style of OD&D "easy mode" and "hard mode".