The pros of backpacks are many, but as you've pointed out, the downside is bearing weight on your back and getting a sweaty back. My solution has been to attach a box to my bike that is large enough to hold a waterproof backpack. Using this solution I've seen no need to purchase panniers even after living in the rainy Pacific Northwest for a couple years. I love being able to wear the backpack while shopping or if I feel like walking at any time.

Here's the bad news: The box I purchased appears to no longer be available commercially. It's called the Donkey Boxx.

The good news: There are other baskets that are large enough to carry a loaded backpack, but I recommend making sure of this before committing to a purchase. One option is using a large milk crate and putting it on the rear rack. I initially wanted to do this but I opted not to because this makes mounting the bicycle difficult. I have spoken to a couple people who strap their backpacks to a front rack, known as a Porter Rack. This will make the bike a bit wobbly, especially if the backpack is loaded, but it's one option. Best of luck.