So if I'm getting at the point: you'd swap in some of the up to 4 cards after seeing your opponent, but before the mulligan?
I feel like the first problem with it is simply time. I don't want to have to pick through my deck to figure out what cards to remove, and wait while my opponent does the same. It'd be better to adopt something like the Expert format, where you'll queue with 3 nearly-identical decks, and could choose between the 3 options at start. That could be done a lot more quickly, perhaps in as little as 15 seconds.
I think, mostly, I don't really like it. Being able to slot in counters to certain kinds of decks really skews a playing environment. Like, I don't think sideboards mitigate hard counters that much, and could easily strengthen them.