In D&D 5e roles overlap a lot. A ranger can be a capable healer, a fighter or a cleric could disable traps, druids are excellent scouts, bards could... well could be anything from healing to diplomatic duties to thievery, etc.
Sure, but they don't do those things very well. That's the problem you get when everyone can do (a little of) everything. Nobody does anything particularly well.
Nah, that was in previous versions of D&D. Bards could master any skill, only some rogues could rival them. They also could fulfill any role you can think of if you build them accordingly.
Rangers have healing spirit, something that even clerics do not have, so they are fantastic healers. They only lack mass healing. Even celestial warlocks, bards or some sorcerers have buff and healing capabilities.
Druids have pass without a trace and could turn into animals ( even animals with swimming, flying or burrowing capacities later on), and also have several spells at their disposal to detect enemies. They are one of the top scout class of the game by far. Wizards and Bards excel at it using their familiar to scout ahead. There are several hybrid subclasses that allow fighters or rogues to have access to wizard spells, so they could provide arcane support.
Any character with enough dexterity could use thieving tools to open locks/disable traps, etc. And since there are weapons that use dex for attack and damage, there are fighters, monks or rangers that could be excellent trapspringers.
Paladins, bards or sorcerers could be great faces for the group, due to his high carisma, but any character could learn the dialogue skills. etc etc
I don't buy this. But for the sake of argument, if you are right, then what exactly is the point of having classes? Effectively, every class is considerably the same as at least one other class and maybe more, and all the classes significantly overlap each other. So in truth you have a classless system with fake classes to give the illusion of a class-based system. Nope. Don't buy it at all. A cornerstone of D&D has always been its distinctive class-based system, and although 5e has weakened the distinctiveness of classes it has not erased their distinctiveness the way you describe it.
Yeah I don't buy this either. All the things you listed _Vic_ are unique abilities to each classes, it doesn't make them better.
A bard was a master of skill, yes, and it was ITS strength. Fullfilling any role ADEQUATELY if build accordingly? Yeah I can see that. Being better in said role than the class it emulates? Nah man, just nah.
The ranger's healing spirit, the druid's pass without trace, the thief and fighter's sub classes that allow them to use wizard spells, the paladin's healing abilities...all of these things you mention are abilities that DEFINE a class, allows it to have a certain flavor and be able to cover more ground inside a party and to be able to help where needed. However they will never equal the class whose primary abilities it copies. I wouldn't trust a ranger to support the healing needs of a party like a cleric could. No class comes close to a fighter's close quarter capabilities and sheer number of feats. The wizard remains the absolute master of magic even if bards can cast some arcane spells ans even if every class can pick an odd lock, the thief is still the master backstabber and has access to feats that makes a thief, well, a real thief.
I still think AD&D 2nd was where the classes were the most defined. However, the classes are still really well defined in 5E.