The 5e system is already pretty flexible - additional class flexibility isn't needed even with a 4-person-party restriction.
So my takeaway is that these threads are largely melodramatic then.
To be fair, yes there is a lot of melodrama and hyperbole. But the fact that the 5e system is flexible doesn't mean that classes should be made even more flexible. Certain classes still excel at certain things and should feel different to play. At some point the line is crossed where classes are more similar than they are different, which removes a core (or classic, if you take issue with "core") aspect of D&D.
The location of this line is an opinion. Bonus action hide/dash being given to everyone instead of rogues? Scrolls usable by everyone instead of the appropriate casters? Thrown potions + scroll usage + Help action making everyone an amazing healer? High ground advantage + shove encouraging every class to play a similar style (ranged attacks + shove)? I wouldn't say any one of the above is sufficient, but all?
And "classes should be distinct" is just one of many arguments for More D&D 5e Rules. E.g., there's also the Balance Argument: Quicken/Haste allowing you to cast a two fully leveled spell is really powerful, Shove OHKOs, changes to enemy HP and AC but not STs nerfs ST spells, surfaces causing auto-damage has cascading effects, the whac-a-mole system of healing downed characters, etc.
