I generally use the spare tube first. Sometimes something goes wrong. Maybe you damage the valve while trying to inflate it with your mini pump. Maybe a bit gets pinched in the tire bead. Maybe you didn't remember to get the shard of glass or whatever out of your tire. It's not very likely that you'll get a second flat randomly down the road (though it can happen), but there is a good chance that you get a second flat that is directly related to the first flat.

So why not go to the patch first and not carry a tube? Well, it's more of a hassle on the road. If it's raining making a good repair can be tricky. And some things just aren't patchable.