What's the point of intercepting an aircraft?
Military interception usually happens after failure to make the aircraft comply by other means (such as radio, light signals, flares). So, first and foremost it is one way to do visual communications, which is usually hard for the pilot to miss. The messages for follow (wide level turn), land (low pass, landing gear extended), and continue on course (climbing turn) are well established (possibly even internationally?) and all pilots should know them, and are probably enough to defuse most situations. Not to mention that you should try to establish radio communications on 121.5 if you're being intercepted.

I'd wager a guess that the most common cause for interception is that a pilot has strayed into restricted airspace without talking to anyone on the radio, without any malicious intent.

If the pilot ignores the messages, there's always the option of using force, if the risk to occupants and collateral on the ground is acceptable.