Printer and Scanner with Time Capsule
You could connect your multifunction printer via USB to a computer and use printer sharing to enable other machines to print through it. The downside is, as you point out, it is often less reliable, and you can only print from other computers when the host computer is on.

You could connect through your Time Capsule. Some multifunction printers only support scanning when directly connected to a computer.

You could get a new wireless multifunction printer that supports scanning wireless. This requires a more sophisticated machine, as the scanned documents have to go somewhere.

It is possible there is a way to make your multifunction printer work as a scanner while attached to the Time Capsule, but it's a property of the device, and you didn't specify what you're using.

So in the absence of more information in your question, this is my answer.