Over time and especially within the last years, it has become trendy to criticize Dungeons & Dragons systems that have been part of the game since it was first published in 1974. Aside from people attacking the "confusing" (it's not) different usages of the term "level" for classes, spells, and dungeons and especially the disconnect between class level and spell level, the overall magic system that Gary Gygax introduced also gets its fair share of scoff and ridicule.
In this article I am going to try my best to a) defend it and b) explain how to rethink it so that it properly makes sense and shows why it is a great system for Dungeons & Dragons.
As the above "Wizard and Dragon" cover art by Jeff Easley (AD&D 2e DMG) perfectly illustrates (pun kind of intended), old-school D&D magic-users could become truly powerful. They bend the reality of the universe to their will. But Gygax knew that magic and its wielders needed limitations. As some, though not all, modern D&D players know, the magic system of Dungeons & Dragons is heavily inspired by (directly taken from) The Dying Earth by Jack Vance. It is very much a "hard' magic system, as Brandon Sanderson would classify it. Magic and its users have very strict rules of use and thus limits to their powers...at least initially. Magic-users are also not as commonplace in these worlds. Wizards were frail and week at the beginning of their careers and thus most never survived to the high power levels (just ask my 13-year-old son with his 1 HP magic-user in Old-School Essentials). But that is by design...brilliant design. You know that when you encounter a magic-user in these worlds they could be immensely powerful and your defenses against them are limited at times.
Many modern D&D players find the old-school system (and even the 5e system to a degree) of magic to be too rigid and limiting. It certainly is more limiting than other magic systems that are out there. I love the magic systems from Symbaroum and Warhammer Fantasy Roleplay. The exchange of dark corruption for the ability to wield magic is a great system and allows almost any power level of character to cast most spells (or at least attempt to do so). That's not the case in old-school Dungeons & Dragons. You have a very limited amount of spells at your disposal and you better know when and how to use them. Magic in D&D since 3rd Edition has become much less restrictive and more free-form. Cantrips massively altered how magic-users worked and, I would argue, made the magic system less meaningful.
In D&D 5e, casters don't have to worry too much about planning and conserving their power, since even a level 1 wizard can use combat-, resource-, and buffing spells as cantrips. Modern D&D has made the magic system less mysterious and "magical" on the one hand and also reduced the danger & power of casters on the other hand. Players of modern d20 games blow through spells and don't worry too much about it. It's, at best, formulaic. Many spells have also become less powerful in an attempt to balance the game. Sleep is the best example of this. In modern D&D you determine the amount of HP of creatures it is effective against, whereas in old-school D&D you determine the amount of HD of creatures. Using Sleep in a game like Old-School Essentials is much more powerful than in D&D 5e, but your usage needs to be calculated.So how should one view the D&D magic system to understand its brilliance? For one, go back to an old-school system approach of limiting the initial usage of magic. No more cantrips! You immediately think of your spell selection as a powerful resource that must cultivated, expanded, and used conservatively. If you survive and grow in levels, you can gain more powerful spells (ideally by finding them) until you are amongst the very rare elite mages of your world. Magic-user survivability must also be more limited. Therefore, I recommend going with 1d4 HD again.