I will agree with your first point and argue the second. Tradition does expand out quicker than Progress in the early game. However, its the infrastructure part that Progress shines in. Progress has more workers, more gold, more production, and more food for those satellite cities. Progress satellites gain infrastructure at a faster pace than Tradition ones do, that's its main strength.
More food? Do you forgot that Tradition has extra city growth for every city. From the starting policy, and growing more powerful with each policy, instead of a flat 3 food, in a later policy. Tradition secondary cities reliably out pace Progress cities in terms of population.