My local primary school has the accelerated reader scheme meaning that 30 minutes every day are scheduled in for reading. The class of 30 gets divided up so the teacher & TA (if lucky enough to have one) listen to a child read and then ask questions to check comprehension.
The accelerated reader scheme means that when they finish a book they have to sit a comprehension test on it and if they pass 3 books they move up a level.
We have found that this really helps push children to firstly finish a book and choose books that they wouldn't normally pick. OP just keep listening to your child read, ask questions about characters, what do you think will happen next/why does he feel that way/what would you do in this situation/what do you think this word means/do you think X is a good friend? In later years we ask about sentence structure like embedded clauses.
I volunteer in the primary school. I am a qualified TA but just give my time for free. If all I did was listen to children read my life would be very easy. But I love what I do. Having worked in the school for a few years I am trusted with intervention work, working with small groups or 1 to 1 for maths and literacy. I mark work as they do it or later to help ease the workload of the teacher. I make cups of tea at break time and staff fall over themselves with gratitude.
I think it would be helpful if parents did volunteer into a class. I had to undergo a course first to cover policy such as first aid/safeguarding and DBS checked before starting but I think some parents just think teachers teach. They don't see lesson planning, behaviour management, marking, assessing, differentiated work.