The brakes on automatic cars get more use than they do on manual gearbox cars because they don't get the benefit of the engine braking effect like they do on a manual. As long as the brakes are working OK no-one at the MOT garage is actually going to measure the thickness of the discs are they? A new disc (from memory) will probably be about 21mm thick.
I have used discs that were slightly below minimum in the past, as long as they were smooth and not warped they are normally OK a mm below spec, they may heat up a bit more during heavy braking but its not something to panic about. Modern pads (no asbestos) tend to be harder than they were in the past and probably the discs are softer to maintain braking force, normally discs will need to be replaced once to every two pad changes which could be from 60 to 70K on a manual, less on an automatic.
My manual 1.4 SE is just about 80K so I will be fitting new discs and pads soon (as soon as the weather warms up that is!). On my previous Civic I only replaced the discs at 100K, but then I don't do a lot of city driving, I am pretty light on the brakes and tend to coast up to islands and junctions. Just remember if you do use the brakes very lightly all the time you can get a glaze building up on the disc / drum (not so prevalent with the hard pads / soft discs now in use) you may have to occasionally do an 'emergency stop' from a reasonable speed (on an empty road
) to heat everything up a bit and check that your brakes really will work when you need them.
Enjoy your Jazz and don't get bogged down with the little things
But do remember that every time you use the brakes you are wasting the fuel you used to accelerate the car, and the harder you brake the more fuel you are wasting!