Approach #2, the Steam approach, is basically what we do (although without using an external service like Steam). We check that your copy of Army Builder is valid when you install or update it. After that, you're free to use it as much as you want without requiring an internet connection. You certainly don't need an internet connection every time you launch the program, unless you want to download program or data file updates.
Approaches #1 and #3 have obvious flaws which you mentioned. Unfortunately giving someone a week's "grace period" exposes us in a number of ways. For example, what happens if someone simply uninstalls and reinstalls Army Builder after those 10 days? What happens if they just set their clock back or forward? What happens if their system clock is failing?
Those are all problems that can be solved, but it makes the process more complicated and error-prone. So, we decided to go with a simpler system - either you're licensed, or you aren't. Licensing requires an internet connection when you update the program, but that's it - otherwise you can run disconnected.
Regarding the number of licenses - while you wouldn't share your licenses with your friends, sadly many people feel differently. Every year at Gen Con, we have people in the booth discussing how they'll buy one copy of our software and share it between them - we think a limit of 2 is very reasonable, and additional licenses are available for $10 each if you have more computers.
Hope this helps explain why we do things this way
