Why do my bicycle brakes get worse and feel more 'squishy" over time?
On most cable disc brake systems there's a moving pad and a fixed pad.  The moving pad presses against the rotor and bends it slightly towards the fixed pad.  The rotor is made of rather springy steel, and is probably where the feeling you experience comes from.

The barrel adjuster only addresses wear to the moving pad, but the fixed pad also wears in use. The rotor has to bend more to contact the worn fixed pad. This means that tightening up the fixed pad is necessary (about every other time I tighten the barrel adjuster on mine, but it depends on the pads and mechanism).  It can be a bit of a pain as it's not very easy to get at.