It would be nice some weekend to have everything unlocked, but not each beta weekend. I think that the feedback and data on the progress it is important. In fact, I am more worried about being able to rush the content in the first week.
Most cards seem like they have little to no impact. The weapons are nice and they have an impact. I would like more differences between different rarities, so the rare ones would be stronger.
I don't think you would notice a big difference between going without cards or with cards. I played some games without any of them because I was shuffling cards and a match message popped up so I couldn't select cards for that game. No difference playing with them or without them, lots of cards are really situational and some cards help and some others help too little for being able to select only one of them.
Maybe the devs want the cards to have little impact, but when you have to collect tokens and you can pay to lock cards and all that, it looks like the cards system should be much more important and they should have a bigger impact than they have. There is hardly any theorycrafting with the current system.