Well the thing is, crystals are the only trustworthy way to keep time, and they run at a pretty high frequency so they need to be frequency_divided with the 4040 counters.. Even timer chips need counters to get a period longer than a few seconds..
So we do need the crystal, we need the counters, and we need the flip-flop since our signals are pulses, and they hold their value once set..
I suppose IC6 could be eliminated, and altered so that the relay is powered immediately when the circuit is started, but we still need IC7 to set the turn off time.. It might be possible to eliminate a counter in the crystal area, but with both of them the pulses are calibrated to 1 minute which really makes usage easier..
There are other ways to cascade the counters.. eg, one to measure day length with one to measure on-time slaved after it, but this opposable setup is probably roughly as simple as any method would be.. It really isn't that complicated as far as circuits go..
If you're confused about how the counters reset themselves, notice their outputs are all tied to 9V, and to the reset pin.. when all the tied outputs are high, they stop sinking that 9V, so it triggers the reset and it starts counting again..