Then I'm sorry I'm late to the party. As mentioned I picked up the books because there was one specific story I wanted to tell. The argument that there are changes in the system between the settings isn't a very strong one, FFG designed these games, they could have easily designed the core rule, which do all run off the same basic system, to be totally modular, with little to no extra effort.
A Kroot, a Commissar, and a Genestealer simply do not meet each other in a tavern in 40k, and decide to go "clear out" the Eye of Terror. The lines produced by FFG do an excellent job of finding the few situations where individuals of diverse backgrounds meet together to perform monumental tasks, within the 40k setting. It is meaningful to note at this point that 40k is one of those settings where for the average individual, life is quite restrictive. Further, it is quite uncommon for RPG sized groups of people to do much of anything interplanetary in the setting (this is of course assuming, that in a WH40k RPG, being able to go from planet to planet is something to be grasped). Therefore, settings tailored to these few groups that do have the ability to command their destiny are the ones we see the core books written about (well, up until we got OW, that one is a bit odd in this sense)
Also, note, your only "issue" here is about having to buy 2 cores, instead of 1 core and 1 splat book. And you're requesting a system where everyone has to buy at least 1 core and 1 splat, instead of just 1 core book. (this is assuming you're trying to point out the benefits of having a generic "Core Rules" which only explain the basics of how play works/combat/generic character creation/generic armoury/generic background, and then splat books that fill out the setting for a particularly workable theme (e.g. the Inquisition, Rogue Traders, the Deathwatch, Chaos Warbands, etc.)).
Core rules = $60 (of course, what you're asking for could be cheaper, but in all likelihood it would still have full combat, partial psychic, partial armoury, skills, talents, generic how to play, generic character creation, a "How to GM" section, a full fluff writeup of 40k, and probably a generic adversaries section. So I think $50-$60 is easily justified)
Splat Book = $40/$50 (varying by size. for what you're asking, $50 is entirely possible)
If everyone must buy 1 splat/1 core, its $100 to get started in the system.
If everyone must buy 1 core, then its $60 to get started. It is to the advantage of most people, to only have to buy 1 core. Those of us who desire to see more broader settings can just eat the $10 cost of buying a second core book.
Also, its a nice way to subtly alter the rules over time, DH's core rules are quite different from OW's core rules. You most certainly do not need to get the GM screen, the one for DH would still work quite well for your purposes.
Much of the spirit of the books would be lost as well, as they're often written to the theme of the setting. For example, read the section based on what happens when you suffer hand/foot/arm/leg/eye loss, it is hilarious, and quite notably, written for the specific setting. If the game went generic, this humor could easily be lost, and the core rulebook would quite likely become this dry thing that only details the mechanics. On the other hand, it could be bloated by trying to write to each "point of view" in the rules.