Question: I'm doing a total kitchen renovation with solid hardwood flooring. Do I go hardwood all the way under the cabinets to the wall or stop just past the toe kick and finish the rest with ply of the same thickness?

Answer: 
You can do either, but in my opinion it's better to use plywood as the base because:

* it's a lot cheaper than hardwood flooring.
* if you need to replace the hardwood flooring at some point in the future, it will be a lot easier to remove just the hardwoods: if you run planks under the cabinets, you'll have to cut them off where they go under the toe kick which will be a lot trickier with the cabinets in place.
I ran mine all the way to the wall. Turned out to be a good thing because I made a cabinet change which pushed everything down six inches.