It's clear they were thinking PC-first by the time of the 386SX, because it's clearly product targeted for a specific niche in the PC hardware market-- teasing "you can have 386-enhanced Windows or OS/2" to people who would otherwise be served well by an equally clocked 286.
It seems like we're suddenly mixing up technologies here.
While it's certainly no doubt true that the dominance of the IBM PC and MS-DOS software forced Intel to realize that they needed to have a compatibility mechanism like VM86 mode in the 386 to viably position the product as the natural growth/update path for the personal computer market as a whole, this actually has very little to do with what was being discussed, which is "why didn't Intel make something like the 80186 but PC Compatible".
VM86 mode is an ISA extension that exists to enable the 386 to freely mix at a "task level" legacy real-mode 8086 code with native protected mode software, IE, it provides an easy hardware-enforced mechanism for an OS designer to go hog-wild building the next generation of OS while still letting users drag their old DOS software along for the ride. The 286 was roasted repeatedly and ruthlessly for not allowing this. (Recall the famous Bill Gates quote about the 286 being a "Brain-Dead Chip?". It was the lack of backwards compatibility once switched into protected mode that he was talking about.)
Some companies actually *tried* to work around the 286's issues by exploiting "Unreal Mode", IE, directly messing around with the registers of the CPU in undocumented ways, but these techniques were slow, rickety, and broke on some steppings of the 286 chip. Intel took it on the chin really hard for this limitation, and explicitly designed the 386 based on the feedback.
To be clear, maybe the 286's backwards compatibility limitations looked perfectly reasonable in 1982 for vaguely similar reasons as the 186's hardware setup seemed "fine". It's not as if the 286 is completely incapable of running real-mode code in Protected mode, you can write "well-behaved" code that can run in either Real or Protected mode, just like you can write software that runs perfectly fine on either an IBM PC or a Tandy 2000; if you do everything through documented APIs then user code doesn't need to care about the underlying hardware or OS. Maybe some of the blame should land on IBM for cursing the IBM PC with such lousy BIOS APIs for accessing hardware like the screen and serial ports that it pretty much forced software writers to go straight to the jugular and thus encouraged the development of a software base that almost uniformly broke all the rules of "good behavior", but on the flip side, well, the 80286 didn't see the light of day until people had been building the PC/MS-DOS software base for multiple years; imposing new rules after the game has already started almost never works out.
Anyway, the point I'm laboring to get to is while, sure, the VM86 extensions were an important concession to the realities of the PC software market, on a "system architecture" level the problem they're solving is nothing like the "making a CPU more like a SoC" thing. The 386 CPU is still just a CPU, it doesn't incorporate any of the chipset features that were being talked about here. Intel did start selling by this time companion support chips (IE, "Chipset" components) that largely complied with the ad-hoc PC standards in terms of hardware addressing, but the CPU itself still was just a CPU. Off the top of my head I think you have to get all the way into the Pentium era with the P54C's inclusion of an onboard APIC to really start arguing the CPU was swallowing up chipset functions, and even then it's still nowhere close to being a "SoC", or even what the 80186 is.
Bluntly I'd say again the reason Intel never bothered making an XT-class semi-SoC is simply because by the time it became so obvious that PC compatibility was such a make or break deal Intel had zero interest in perpetuating the market life of 8086-class machines. Second-sourced 8088/86s were everywhere and other companies were already doing integrated chipsets, where's the money to be made for Intel here? They'd much rather come up with reasons to upsell you on a better, more expensive (and more profitable) computer, especially if they're the only one who can sell you the chips for it. (Which is exactly what they tried to pull off with the 80386.)