eg. i exercise hamstrings when i do deadlifts, but then i also want to isolate the hamstrings and give them extra work (bc on deadlifts i'm bottlenecked on lower back strength, so hamstrings don't get properly destroyed), so i use the hamstring curl machine
i also use a pulley for triceps curls, bc i don't enjoy doing triceps curls with a dumbbell (but a dumbbell is perfectly fine for this)
same with pec flies
and i use a pulley for face pulls and lat pushdowns bc it's not clear to me how you'd do that with free weights at all
actually lat pushdowns is another case of isolating a muscle that gets a workout otherwise anyway, eg with pullups
and face pulls you could probably do with dumbbells if you lie on a tall bench on your stomach
in conclusion, free weights only = probably completely fine
there's way too many squats and no vertical pull, so i switched the squats in one of the days for lat pulldowns
(there's both horizontal push (bench) and pull (rows) and vertical push (overhead press) but no vertical pull)
what about pullups? i guess it's not that important
you should probably start hitting a plateau in a few months anyway and then you ideally switch to a more intermediate program