Does never using the easy front gear give a better workout? I have a road bike with a 52/36 crankset. I make it a point to never use the easy gear because I think that it gives me a better workout when climbing hills. Another reason I don't use it is because the chain rubs on the front derailleur when going from the 36 on the front to the 12 on the back. 

Is my theory of getting a better workout correct? Is there any good reason for me to not do this other than putting more wear on the gear?

There is only about 3 hills in my daily commute where I sometimes want to downshift into the easy gear.
It is not necessarily "good" for your workout. If you drop into the 'easy' gear, you obviously have to pedal faster to maintain your speed. Going at a slower cadence in a higher gear will just trash your knees after awhile.

Select the gear that yields a similar cadence as when you are riding on the flats, while maintaining a similar energy expenditure.

Your chain rubbing problems should be solved by adjusting your derailuer and properly maintaining your bike.