Actually several Pentium 4/D era motherboards (945 chipset) could accept some Core 2 processors after a BIOS update, and several early C2D boards could be updated to take later 45 nm Core 2 Quad's.
Not a single Pentium 4 era motherboard accepted Core 2 because Intel changed specifications just before Core 2 launch. It's not chipset but motherboard VRM that matters, even i915 could support Core 2 if VRM is OK. As VRM is the key, many Pentium 4 motherboards that were supposed to support Core 2 Duo did not do it (many even advertised to have support) and so it's safe to say Pentium 4 motherboards do not support Core 2.
This is what I mean, Pentium 4 motherboard with promised Core 2 support: https://www.asus.com/Motherboards/P5WD2E_Premium/specifications/
"Support Intel next generation 65nm CPU"
Well, no support for any Core 2.
Those early Core 2 motherboard had so low FSB that they could only support slowest Core 2 quads, at best.
Really it was dependent on the manufacturer. Over the 6 years or so that socket was current (2004-2010) manufacturing process shrank from 90 nm to 65 nm to 45 nm, covered two entirely different architectures (Netburst and Core) and FSB's varied from 533 mhz to 1333 mhz. So it's not entirely unexpected that a 2004 motherboard wouldn't take a 2010 chip...
There were at least 4 "versions" of LGA775 socket. Not exactly as socket remained physically same but in practice:
- LGA775 for single core Pentium 4's
- LGA775 for dual core Pentium 4's
At this point compatibility was broken, Pentium 4 motherboards did not support Core 2
- LGA775 for slowest Core 2 duo's and with some extent slowest Core 2 Quads
At this point many boards dropped support for Pentium 4
- LGA775 for faster Core 2 Duos and Quads
So basically there was no point keeping socket same for as new CPU's would still require new motherboard.
The situation with Kaby Lake and Coffee Lake is rather different. No die shrink, a minor microarchitecture update and two extra cores added.
As I said though, it's all speculation at this point. We will see in due course what the answer is.
Speculation still of course but considering we are talking about Intel, I wouldn't expect much for supporting old motherboards with new CPU