But as far as overlap... I don't think any of that is indicative of needing to create a bin to put certain classes in. After all... if you take a look at the 3E spell lists... there's quite a bit of overlap between the Wizard and Cleric spell lists. And no one would say that they are in the same bin. And you can add Druid, Paladin, and Bard to those lists too. Cleric, Paladin and Sorcerer/Wizard all have Protection From Evil on their spell list. Bard, Cleric and Sorcerer/Wizard all have Hold Person. Cleric, Druid, and Sorcerer/Wizard all have Obscuring Mist. Bard, Cleric, Druid, Paladin, and Ranger all have Cure Light Wounds.
First off, the arcane/divine split doesn't prevent you from having spells open to everyone, because most effects are not arcane- or divine-only; as I mentioned, there are several things that arcane and divine casters have traditionally had in common but have excelled at in different ways. You can have a wizard-only list, an arcane-only list, and an "everyone" list, and in fact having that "everyone" list only serves to highlight the differences better. Having some spells open to everyone doesn't negate the fact that
fireball is a very "arcane" spell and
restoration a very "divine" spell while
animate dead is both--and I'd argue that having the cleric be a better animator because he has both
animate dead and Rebuke Undead is a better strategy than giving him a different version of
animate dead.
Second, the hybrid classes' blurring of power source lines is part of their point. The bard gets some healing because it used to be divine and is now arcane; the ranger has some arcane and some divine spells because it started off with both magic-user and druid spells; the shugenja has some arcane spells because it was the primary caster in Rokugan (a setting without the traditional full casters) before being integrated into "normal" D&D. Those hybrid classes are exactly the ones with different "feels" in different editions: the 1e ranger is an Aragorn-like fighter-plus-magical-training type, the 2e and 3e rangers are a Drizzt-like champion-of-nature type, and the 4e ranger is a Legolas-like archer without magic. The 1e bard is a Celtic warrior-poet who uses druidic magic, the 2e bard is a wandering scholar who uses wizard magic, the 3e bard is a jack-of-all-trades who uses a little bit of both types of magic, and the 4e bard is an inspiring performer who is back to arcane-only but has his own list.
If 5e is going to appeal to everyone and make all class concepts possible, they can't really try to cram all of those concepts into the same class. Conceptually, you add magical music on top of a druid/fighter to remake the 1e bard, on top of a rogue/wizard to remake the 2e or 3e bard, or on top of a fighter/wizard to remake the 4e bard; similarly, the 1e ranger is basically a fighter with minor arcane and divine casting, the 2e and 3e rangers are basically a fighter/druid, and the 4e ranger is basically a fighter. Any of those individual classes either fits pretty squarely in one of the arcane or divine camp or is explicitly a hybrid/jack-of-all-trades, and if WotC is going to follow through on its promise to have ways to make every core class from every edition in the first PHB, they're going to have to either do a multiclassing+specialty approach like that, make different versions of a class for each, make big unwieldy classes than can do any version but none of them well, or disappoint a segment of the player base.
And finally, regarding "magic is magic":
Which there again tells me that magic is magic. One big lump of energy that is accessed in a myriad of ways. And just because you can cast certain spells does not mean you are an Arcane class or a Divine class or anything like that. Because many spells cut across Arcane and Divine. So again... I don't see the point in trying to divide classes up when there's no actual logical binds that tie them together. It's only artificial ones that we keep in our heads from previous editions under the belief we someone need to have them in the game.
But I don't believe that's true.
By that reasoning, a fighter is the same as a rogue, really, because there's plenty of overlap between them and they basically do the same thing (stab things in combat and use skills outside of combat). Alternatively, the fighter, rogue, monk, ranger, and all other classes shouldn't share expertise dice, common maneuvers, or any other similar mechanics because they all do their own different thing in their own different ways. Yes, you
can boil things down to either "either you're magical or nonmagical, pick one" or "no two classes share things in common" but the former is basically point buy, the latter is very hard on customization, and neither is really D&D-ish.
If they're going to both come up with "iconic" versions of each class that satisfy fans of different editions, particularly AD&D, and also follow through on the "modularity" buzzword they keep throwing out there, then those classes
do have logical binds that tie them together and there
are benefits to categorizing things as arcane or divine. Neither the "every class has a completely different list" approach of 4e or your suggestion, or the "everyone can access everything, it's just the resource systems that are different" approach that has been suggested in some of the 5e columns, will satisfy either of their design goals. They need both some common spells (to cut down on redundancy and improve consistency) and some unique spells (to help define classes and to add variety), and the existing arcane/divine split is the most traditional and (I think) best way to do that.