HI Dale Everything one learns has a place. What determines its usefulness to each person depends on - mainly - their primary goal .Is it to play written classical music? Is it to progress in creating and understanding chord patterns to create accompaniments to popular ballad type songs? Or Blues, or rock? (each have different accompaniment styles )
I usually advise students to tell me what they are most interested in aiming towards. The pop
left hand course happens to be a little easier than a rock style
left hand ( faster therefore another factor making that harder) or blues (slower but always requiring 2 simultaneous fingers in left hand - though a beginners version can be done single left hand notes ) and so on ..So learning at least the basics of a pop style accompaniment is preferable to starting with jazz blues or rock.
Judging by what you’ve said personally - it sounds like
1) Reading in your left hand should be a priority - you should download the "s
hoot down the notes " program -
2) Learning right hand chords is an advanced step when you still are not fluently playing at least basic left hand chord patterns - as you are going to have to not only play the right hand chords but also fit in the melodic line - all in the right hand
Generally if focusing on that method ( carrying the chord in the right hand ) rather than the goals of
the left hand pop ballad intro course which focus on improving left hand technique quite rapidly, another simpler approach is used on left hand . Then one focus for instance on just playing left hand octaves on the first beat ion beginning rather than fifths or creating a left hand rhythm pattern - only a very advanced player could achieve right hand chord/ melody integration as well as left hand rhythmic 5th and octave patterns
One has to remember a teacher can only go on what you tell them. Also however some teachers have predefined methods and don’t like to step outside of that .....When it comes to chord patterns a teacher might ( teacher orientated towards contemporary music )- have their own system for learning accompaniment styles
Re your question 2 octave scale patterns - .If one can play one octave moving the hand and independent fingers are being achieved
Playing left and right hand together, because the hands move at different times. it would be useful to achieving chord patterns but only in a roundabout way - once again one needs to set priorities - so you should discuss those with your teacher if you haven’t already ......a suggestion might be you could for instance choose to do just one key for now leaving you time to focus on other things too , rather than spending 30 mins or so struggling with different keys.....but you should discuss with your teacher - I’ve had pupils [play contemporary music very successfully without playing 2 octave scales without playing 2 octave scales hands together ....i don’t want to put a spanner in the works for you -

but you did ask.
