I've known people to freeze bagels. Apparently they toast more or less equivalently compared to bagels stored above freezing.

This is correct. I don't eat enough bread (or bagels) to warrant buying entire loaves at a time, even, and they will grow mold before I can eat them. Freezing them works great for me and prevents mold.

Yeah, you can't tell the difference. You can even microwave them for 30 seconds instead of slowly defrosting and if you're toasting you can't really tell the difference.