Playing tight to a beat can be an odd challenge for many, but everybody loves the result when you crack it, as all of a sudden your notes sound like music. Then I play the second guitar layer with you, maybe even sing and we sound like a full band. Of course this will be started at a slow tempo and then notched up to drive a challenge into your fingers.
Not a feature of regular tutors.
Following a rhythm will make a huge difference to your progress as it keeps you out of the trap of changing chords at your own convenience with stoppages between chords and when both hands follow a rhythm they synchronise much better. It also helps generate a musical ear because rather than distracted by other instrument's sounds, you get involved and responsive with each other's rhythms and dynamics.
Not a feature of regular tutors.