5e has a fairly robust and extremely accessible combat mini game that is a lot of fun to play.
It's core model of a team of adventurers tackling heroic adventures is extremely casual player friendly. The drop in Adventurers League format shows the power of that model to get people in the door.
There's also pretty good adventure support.
It's a great game with loads of mainstream appeal that is extremely good at what it does.
It's really not anymore flexible from a technical standpoint than any other game, but it does not need to be. It's great st what it does and people like what it does.
I think that a starting analysis, like yours, is actually really helpful when people try and understand what makes D&D
good and why it is popular.
The idea of a team of co-equal adventurers (the party) is engrained in D&D and part & parcel to TTRPGs; it is much easier to envision "the party" in this genre for a number of reasons (the legacy of Tolkien and other fantasy authors being among them) than it is in many other areas.
Needing only one person (the DM) who is rules-savvy and comfortable with narration allows it to be newbie and causal friendly.
The simple, "DM describes environment, players describe what they want to do, DM narrates the results," loop is simple and easy to understand.
The zero-to-hero, gain new abilities and power and items over time, is such a successful and powerful rewards-loop that it is the basis for a good deal of the CRPG industry (and, arguably, even more).
And then, contrary to what you ended with, I believe that the core rules supporting and encouraging multiple modes of play, from variant rules to the interminable TOTM/GRID debate, creates an atmosphere that encourages flexibility in a manner unlike most other TTRPGs.