Or just take out the desired card. When standing at a checkout this
is hardly inconvenient.

You aren't at a checkout you are in the middle of maybe 20 people all pushing top get on the bus or at a barrier gate in the middle of the rush hour. The last thing you want is to hold up a wallet full of credit and debit cards where it can be grabbed let alone the fact that you will be getting jostled by a lot of impatient people.

For security and speed keep the Oyster card separate in the dedicated wallet provided.