There are advantages to Integrated courses but can't think of many - PIC time 50hrs less than Modular route for CPL.
I agree with your arguments except for the above one. Less pic and total time is a disadvantage if the cost is not reduced to match the lower requirement.
The greatest advantage of modular is that you get to acquire autonomy, sense of initiative. There's not always someone checking on you, making sure you're fine as in integrated schools. In modular, you book your own courses, your aircraft, your instructors, prepare navs to places you decide to go, monitor your budget, think of ways to achieve your goal (money-wise) and look for schools you think suit your needs, etc...
That in itself reflects initiative, engagement and motivation.