It appears that the food I offer to Krishna is always untouched. There's the same amount left after the offering as before. What's the logic behind offering food to Krishna?

The food is not untouched! It is blessed. Krishna receives the offering, and because He can perform any action with any of His senses He is able to eat with His eyes, He kindly leaves us the food, sometimes! There are histories where the Lord has eaten everything.

Perhaps someday your sincere desire to feed Him will also inspire Him to take the food you offer, but generally He honors our offering and our desire to please Him...and in return He leaves us transformed foodstuffs. Transformed from that which is to be enjoyed by Him to that which is to be enjoyed by us after He has enjoyed it: Maha Prasadam ("the great mercy of the Lord"). Honoring Maha Prasadam is essential to making spiritual advancement.

Hope this is helpful
Your servant,
Laxmimoni dasi