I like this idea (allowing to select deck within faction after seeing opp's faction) very much. I wanted to write a post suggesting it, except I thought not just the factions but the leaders too should be known and not subject to change.
Probably in a separate game mode after release (so that there will be enough players to populate all modes - ranked, non-ranked, and the new one - "adapt mode" ).
Advantages:
1) It will force people to use several decks, not just one. The deck construction part of the game will be much more demanding and interesting.
2) The excitement will rise . Currently, when I select a deck for a game, I already know what strategy I will play, more or less. If I chose something based on buffs and see a Radovid opp, it is like only 20% chance of winning before the play even started. I can't really adapt, the deck is too small. With the new mode, one can adapt on the fly. Going into matchmaking with only the faction (or the leader) known, I am not limiting my choices and can count on an exciting game.
3) There can be bluffs, too. E.g. my Dagon deck is already quite unusual, and I have seen others play non-weather Dagons as well. The "adapt mode" will allow more bluffs at deck-construction stage of the game.
4) Do all factions allow several strategies? I would say so. I had hardly ever seen Skellige control before the latest patch, but with Corail and a few other improvements, I would say the last piece of the puzzle is in place.
Disadvantages:
1) The "adapt mode" is not for beginners. It gives even more advantage to experienced players with all-around solid decks. The solution is easy though: allow this mode from level 10.
2) Even for advanced players, differences in total card collection will be more pronounced. You can craft only a couple of synergetic epics/legendaries and have a very competitive deck based on a specific strategy. However, as soon as not 1 deck but effectively 3-4 decks are playing when you go into matchmaking, the collection has to be richer to stay competitive.