Hi George,
It's possible that you may want or need the slow clock to be slower than half the speed of PHI2. For example, in my Fast PDIP computer I typically run the CPU at about 32MHz, and the I/O module at 8MHz. If I were to use the circuit above, the I/O clock would be 16MHz, which is technically too fast for most EEPROMs. So I really want to divide the clock by more than 2 - perhaps 4, or even 8, to get an I/O speed of 8MHz or 4MHz.
I've been super busy, so I haven't been able to work on Blue August much for the last few weeks. Today I finally had time to build the /4 version of your slow-downer:
It doesn't work quite as expected. Possibly there's something wrong with my expectations

but I don't think it's correct to drive the NAND network with the TC of the second-stage counter.
Rather than think too hard about this, I went ahead and built the other /4 version, with 3 counters. It also doesn't work as expected, in the same way as the simpler one. In addition, it actually seems to work less well than the simpler one, in that PHI2 is 10/2.5 MHz, rather than 20/5 MHz.
I think next I will build the original /2 version to make sure I really understand how it works, and then try modifying it to make a /4 version.