One of the things that has pushed me away from D&D has been how powerful and diverse spellcasters are. I definitely prefer much more focused specialties.
This did cross my mind when I read the topic title. If anything 5e spellcasters are a little too diverse rather than lacking in diversity. Sorcerers and (specially) Warlocks in particular are artificially distinct from wizards, just as an excuse to keep them as separate classes rather than fold them into wizards as a subclass. There's way too many classes in 5e, specially spellcasting classes and specially when the concept of subclasses exists and they could've simply made variants of arcane/divine classes (or even all the warrior classes as well) subclasses of a core class to keep things simple and more manageable.
If anything I would prefer for spellcasting to be standardized and follow consistent core rules, rather than make me keep track of half a dozen variants, with special casting rules and specialized spell lists each. All that crap does is add to bookkeeping and content bloat, making things more difficult to track or improvise, specially from the DM's end. Having numerous spell lists and hundreds of variants of existing spells means that the DM has to constantly stop play to check the book—running through literally hundreds of pages back and forth, checking the class's spell list for available spells, then going through hundred of spell entries—just to find the specific variant the PC or NPC/creature is using now. Even character creation is a freaking pain, when picking your character's known spells
I much prefer the way that Shadowrun handles magic, where magic works the same way for everyone at its core, and everyone has access to the same spells, but differences between traditions (Hermetic vs Shaman of a specific Totem) are handled through special benefits that simply modify how magic for a specific tradition works. Applied to D&D you could use the same core spellcasting system for everyone, but give Clerics bonuses when casting spells tied to their Domains, Druids when using Nature magic, Wizards when casting spells tied to their School specialty, etc.
I do agree with the OP that certain spells can be too limited sometimes, but Steven Mitchell makes a good point about handling enhanced versions of those spells as higher level spell slot versions of the same spell. That's a pretty elegant way to add variety to the existing spells, and allows less limited or more expansive versions without bloating the game up with countless separate variants of the same spell, while also maintaining game balance. Instead, those variations would be found within the core spell itself, making them easier to find and giving you more options for casting existing spells.