A lot of newer CPUs aren't available in DIP packaging which means they won't be usable with a breadboard; the M68k is one of the more unusual ones in that it's available in a 64-pin DIP, the longest common DIP package. E.g. all the x86 processors moved to square packages starting with the 80186/80188, only the 8086/8088 were in DIP.
DIP packages are problematic for high-speed operation since the leads to the pins near the ends are longer than the ones in the middle, creating signal skew; hence the move to square/BGA packages.
That being said, there are microcontrollers with a relatively powerful ARM core and in DIP, but they usually have internal memory and use the pins for peripherals, not as a full memory data/address bus.
Not ARM microcontrollers, which the OP specifically references. NXP’s LPC810 & LPC1114 are really the only game there, and they don't support external memory AFAIK (and it's an M0). Of course, there are a lot of shops bonding an QFP ARM or similar to a slip of PCB that's DIP form factor, but that's not exactly the same.
userbinator's comments are good, and to extend his remarks obviously the solution to clock skew is to simply lower the clock rate. Good luck using a solderless breadboard at 500 MHz digital LOL. But breadboards work just fine at single digit MHz rates.
There is a problem. Many processors use dynamic registers and require a clock above a certain rate to refresh the registers. Yes, no kidding, dynamic ram cells as CPU registers. I know for a fact that the first 386 was dynamic and onlyrated down to 10 or 15 or so MHz (was fooling around with low power ops, if the thing sleeps 90% of the time at 25 MHz, you can't run the chip at 100% utilization at 3 MHz...). You can see a slight mismatch if your CPU registers are only rated down to 15 MHz and you can't reliably breadboard above maybe 5 MHz ... Of course this is analog world and a chip rated to run down to 12 Mhz will almost certainly run at 10 Mhz, maybe even 5 at least sometimes, if you're careful not to run at max temp or min power supply voltage or whatever. And adding to the fun, after (sometimes long after) the first dynamic versions of a CPU come out, someone (often a licensed competitor) makes a fully static version of the chip, sometimes pin compatible. As you can imagine, early on in development, being able to troubleshoot logic by running at a tenth of a Hz is very convenient. If you've ever wondered what "fully static" means on a microcontroller data sheet, well, now you know. And you know why you can't breadboard a classic 80386 but maybe a more recent fully static clone would work.
userbinator's comments about packages are also correct and there is a low speed workaround of carrier to DIP converter boards and proto boards. I've hand soldered many a surface mount TQFP, its very easy. There are many companies selling SMD proto boards, some cheaper, some fancier, but a realistic place to start is googling for "schmartboard", as pretty much if the SMD package exists, they sell a proto board for it, ready for projects like this.
Unfortunately the industry is moving toward BGA packages and the official new hardware to mount those is like $5K although I'm sure I could rig something up much cheaper.
Cheapest possible toaster oven + cheap multimeter thermocouple for manual temperature control + {paste flux, solder paste+stencil} works better than you'd think for soldering BGAs. Even honest-to-goodness reflow ovens can be had on eBay for $300-$400 (search "T962"), which would give you another one or two nines of reliability by circulating the air and having more precise temperature control.
Schmartboard also makes 1.0mm pitch BGA adapter boards, but a lot of the high-end stuff these days is moving to 0.8/0.5/0.4mm pitch. Of course, for those kinds of things, the extra parasitics of an adapter board are probably a no-no in any case.
For prototyping you can also solder BGAs with any hot air rework station. Even if you don't already have one, Atten 858D only costs around $60. Here's an example (not my video): https://www.youtube.com/watch?v=L8EWqWj2srg
I wonder if you could do this with a modern CPU and RAM. What would it look like?