Once upon a time, a lot of effects were siloed into specific classes. If you wanted an area of effect damaging spell, you needed a wizard (or a very high level druid or cleric).
Druids picked up Call Lightning at 3rd level in 1e, but, yeah other AE high-damage had to wait.
If you wanted to fly, teleport, or summon monsters, you needed a wizard. Now, druids are summoners, and clerics can make you fly.
Druids could shapechange into birds or bats at 7th level, Summon Animals from the get-go, Summon Insects, Call Woodland Creatures, & Conjure Elementals, and use Transport Via Plants to teleport a pretty fair distance. I'm actually kinda pleased with 5e's take on the Druid being closer to the original than it's been in a while.
I brought up summon monsters for a reason actually. I LOVE summoners. Always have. Played them all the way back to 2e and probably in 1e as well. I loved how you could call up a small army of minions to do your bidding. Tons of fun for me. Now, the only way i can actually play a summoner is play a Druid? Since when are druids summoners?
1e AD&D. Not the greatest thing to do with 'em, and not able to summon just anything, anywhere, but plenty of it.
By making most of the spell lists very similar - everyone has area effects, everyone has mobility effects, everyone has effects that are similar to each other - and then opening up other classes spell lists to differing classes, 5e has made every caster pretty much the same thing.
I don't think that's fair. Having the same slots/day just makes spells and spell levels remotely practical to try to balance & map against eachother. Sharing some spells saves space, and the price in complexity & confusion is small (personally I find looking up spells in a single alphabetical list annoying compared to the old-school class/level lists, but it's efficient for space and quickly looking up a specific spell). Classes are still differentiated by features and the specific differences found in their spell lists.
Also, Warlocks stand out with a different resource mix, entirely.
To me, this is the problem with ubiquitous magic. It's made all the classes play very similarly to each other.
It may be a bit more pronounced with all the spell re-cycling going on, but casters have always had a comparable set of resources useable for a range of functions, with a lot of practical overlap in all editions, as well as outright sharing spells in most. The differences are achieved in class features and the specific mix of spells and in those unique spells that every class gets (except Sorcerer, EK, & AT who all use sub-sets of the wizard list, IIRC). Setting aside that a specific domain might let you cast fireball, for instance, Flame Strike and Fireball are both AE fire damage, but they're still quite distinctive. Likewise Lightning Bolt and Call Lightning or Fire Bolt, Produce Flame, & Sacred Flame.