Doggone, you're right! I never noticed that. It definitely is an error, and I expect it crept in because of the 65816 which has no phase-2 output. It wouldn't be the first time someone found an error in their WDC's diagrams and spec.s. Which data sheet did you look at? On my older one, it has a delay of up to 40ns from phase-2 input to phase-2 output even for the 10MHz part, and then they reference everything to the input; but 40ns is almost as long as the clock is either high or low, so obviously that won't fly. I looked at a newer data sheet though, and it was fixed.
The phase-2 input and phase-1 output seem to be primarily intended for hanging a crystal or an RC right on the processor itself so an external oscillator is not always needed. It wouldn't make sense to connect the actual processor's innards to the phase-2 input since that one is a Schmitt-trigger input specifically so it can handle the slowly ramping voltage you'd get from a capacitor and resistor connected directly for using the onboard oscillator.

What do you mean by saying 'On my older one...' ?

The 'UMC' logo on chips together with 'W65C02..' is a giveaway here - there's no W65C02 produced by UMC.