Their first priority was – for the most part, Fighter being the big exception – creating archetypes recognizable to players both new and lapsed.
D&D-style Clerics and wizards, and the distinction between D&D Sorcerers and D&D Wizards, and D&D Paladins & Rangers, for that matter, are not recognizable without some prior exposure to D&D - Bards and, especially, Druids are pushing it without some prior exposure to Celtic mythology. (Ironically, while the 5e Ranger apparently flails for any sort of coherent identity, 'ranger' does conjure up things to the non-D&Der not entirely inconsistent with it - guiding people through the wilderness, commando actions, pursuing a quary, etc - even if it's via Rangers of the 'Army,' 'Park' and 'Lone' variety as much or more than the Strider archetype).
So, no, the first priority was evoking the classic game, and classes did that. Two classes went ahead and evoked the less-classic 3.5, but one of them didn't go all that well. :shrug:
With that baseline of success, now it's possible for them to explore some other mechanical options that appeal to veteran players.
What's not to appeal to veteran and returning players in the PH? The classes are mostly familiar from the TSR era, but for two variant Mages from the d20 SRD era. 'Veteran' in the sense of system masters? Turn on feats & MCing.
Well, I'd take the "traditional stuff is only included in 5e" thinking with a grain of salt. Yes, it's mostly based on tradition, but there are notable exceptions...
A very small grain.
Look at the Concentration mechanics. Look at the inclusion of spending hit dice to heal during a short rest. Look at the Monk sub-classes (probably originated in 3e also). Look at the inclusion of Tieflings and Dragonborn.
The Monk was in 1e, as were Assassins, 1e OA had ninjas and Ki and whatnot. Dragonborn evoke the Draconians of 2e. Concentration and HD are very traditional labels, even if there's some less-traditional nuance or functionality to them in 5e.
Look at the Oath of Ancients paladin. Look at the Warlock as originating in the 3e era. Look at the indie-style roleplaying mechanics and Inspiration.
I vaguely remember talk of 'what if there were a 'Druidic Paladin' or 'Nature Paladin' back in the day. And the Sorcerer (and Warlock) in 3.x was a direct outgrowth of dissatisfaction with Vancian that - albeit mostly in the form of 'mana'/spell-point variants - went all the way back, too.
But, yes, Inspiration sticks out like sore thumb, just kinda tacked on. (ouch, painful mixed metaphor, that)
There a very few new-ish things in 5e, but overwhelmingly & intentionally, it evokes the classic game. If it didn't evoke it thoroughly enough, they'd be burning PHs on YouTube.