I have used compostable pots a number of times, with varying levels of success.
My usual trick is to cut a slice down the sides, or poke holes in the bottom when planting out, and do so with them very wet from a fresh watering.
The newspaper pot hack is something I haven't tried, my usual alternative is bog and kitchen roll centres, as they're "bottomless" pots.
Otherwise, a mass of mixed "proper" pots, plus an assortment of yoghurt / cottage cheese and similar containers do their duty. I make quite a bit of use of the segmented trays, including the ones for 3" pots the growers send out to garden centres.
What I do try though, is not to do too much transplanting, as I have loads of pots and a reasonable amount of space, that isn't usually a problem.
Because of the prospect of late frosts and rabbits munching on things, I do grow a few crops & flowers in 3l and 5l pots, like dwarf peas and beans.
I also like hanging baskets, but the watering can be a problem, I keep thinking about rigging up a drip feed system ...