I completely agree, but if anything I believe having a simple core game better facilitates this than starting at a higher complexity level. The "soul", as you say, has less to do with the rules themselves and more to do with aesthetic aspects - the feel of the game, its presentation, etc. Many people who dislike(d) 4E have admitted that a lot of it comes down to presentation first, "video gamey" rules second. We could say that WotC simply put the cart before the horse with 4E and lost their priorities.
The question we need to ask is... "what parts are 'Core', what parts are 'Modules' but should be presented up-front (if any), and what parts a 'Modules' and should be held off for either later chapters in the PH, or held off to second PH altogether"?
Because this presentation of the rules is what will make or break the game... the exact same way (as you mentioned, Merc) that 4E's presentation turned a lot of people off.
Would we consider Backgrounds/skills a part of "Core"? Most BECMIs would absolutely say 'No they are not'. I think Mearls and company would also say that they were not a part of the "simple core", because the simple core is based on Ability Checks, and Backgrounds/skills get layered on top of the Ability Checks.
But let's be honest with ourselves here... what percentage of the 5E populace won't use Backgrounds? They'll stick with the "simple core"? In this day and age... I suspect that that group will be very small. Most players will probably use the "Backgrounds module", because most of the players will last have played 3E, 4E, or a whole host of other RPGs where having skills is the norm. So using Backgrounds in 5E will be seen as the norm as well.
But how then does it get presented to us in the Player's Handbook?
The "Simple core" enthusiasts would say the best way to do it is to hold off ALL modules for further back in the book (if not shunted to another book altogether). But if a so-called "Module" like Backgrounds are incorporated to MOST people's games... what's the real point of shunting them off anywhere? Just to service the 5% of experienced players (of the BECMI variety) who actually won't play anything other than the simple core, and to theoretically present the most basic rules of the game for the theoretically "new player" who is trying to learn the game for the very first time by him or herself just by reading the book? Are those two segments of the populace combined really worth annoying the other 90% of the player base who have to go flipping all across the Player's Handbook to use the rules which, granted, are not part of the "simple core", but ARE a part of most players REGULAR game?
A "simple core" presentation is nice in theory... but shouldn't that really be its own book or boxed set? One that can be JUST that? Nice, short, easy to read, easy to put together? But then leave the Player's Handbook presentation to give us all the rules like we've come to expect right up front, so that the 90% of players who won't just use "simple core" won't have to get pissed off trying to find all the different parts of the game throughout the book?
In my opinion, the first chapter in the first Player's Handbook could certainly have a couple paragraphs that say explicitly "The game can be built in many different ways, from simple to complex. Here are the Core rules and/or modules you can select and incorporate into your game to replicate the feeling of BECMI/AD&D/2E/3E/4E..." but then after that... in each chapter you give the full group of options so that you don't have to chase others down. So the Races chapter has not only Human, Halfling, Dwarf, Elf... but also Half-Elf, Half-Orc, Gnome, Dragonborn etc. The Classes chapter has not only Fighter, Cleric, Rogue, Wizard... but also Barbarian, Bard, Druid, Sorcerer, Warlock etc.
If the player has read Chapter 1, they'll have a pretty good idea of what they want to use (non core races and classes and/or Backgrounds and/or Specialties/feats and/or style of spellcasting and/or healing & hit point models etc.) and will know enough to just skip over those rules that come up in each chapter that they don't plan to use.
That makes the most sense to me in terms of presentation. And does the least harm to anyone's ego, thinking that WotC isn't concerned with how they themselves play their Dungeons & Dragons game.