Can I control a Z84 counter timer circuit with Arduino? Link to pin description and to the Datasheet.

I'm thinking about connecting channel outputs to LEDs and control the clock with IO-Arduino or a 555: I would program it with a 595 register.

Can someone explain me why this is a bad idea?
I wouldn't say it was a "bad" idea - pointless maybe, but not "bad". A good learning experience if nothing else.