I agree with @solonafir. Just make a toggle in the options that can set what you want to be the default. Seems like that would solve this issue without incident, and if there needs to be some sort of tutorial to make things clear to new players, everything should basically be fine (and regardless, if the option is apparent enough, it will easily be ‘discoverable,’ as they say).
Clearly, people have concern over the current setup, but there are also plenty of people who would prefer having their whole collection always available or those (newer players) would not realize they had some of the non-standard cards in their collection (not to mention all the cards removed from the core set that are now only craftable…). Therefore, the best solution should be one that let’s the players decide for their own preferences, or at least some way to be presented with the choice, say, when going into your collection (for the first time in a given play session, or however that would work out).
Also, speaking to @boronian, I think being able to change the default can work so long as new players are well informed and the toggle, option, or whatever the final form of changing the (default) view between standard and all cards is clear and accessible (perhaps right next to the search you can click between standard and all cards, either in addition to being able to change the default or as the solution itself, since of all the thing one would narrow the collection by that one can do already, standard <~> all cards seems important enough to warrant a position right on the collection page without needing to open another menu).
