IPhone won’t ring, only vibrates

Without jailbreaking, your only option is the network operator's (AT&T, Verizon, etc) blacklist option. There may be a monthly fee, $5/mo on AT&T for example, but will allow you block receiving calls from any number you like. iBlacklist will work if your phone is jailbroken, but it costs $11.99 - a little high in my opinion.

It's my understanding that this is by design.

Do Not Disturb mode is meant to be active when the phone is not actively in use. The idea behind it is that, if the phone is unlocked and you are working with it, you do in fact WANT to be notified of a new item. However, when the phone is locked and dormant, the logic is that you no longer wish to be disturbed, and it will suppress vibration / notification indicators.

So for example, if you are sleeping, and DND is on, then it will remain silent, and not vibrate. If you roll over, pick up your phone to check messages, and it's active, the DND will still allow vibrate to indicate new messages while you are using it.