Completely agree. As I said I'm thrifty and cheap, I don't expect a CC to change that. I like my debit card, but I want fraud protection, one monthly bill for day-to-day purchases, cash back, etc. Just seems like a better idea to use the CC daily than the debit.
I still don't get how interest is only accumulated on purchases older than the current month, though. If you are charged interest on your average daily balance, that number is a mixture of last month's balance and new purchases this month. How is it picked apart so that the next statement is last month's balance + interest on last month's balance + new purchases without interest?