When we try to move a bike with its brakes on, the wheels of the bike can only skid. This is because there is sliding friction, which is larger than rolling friction.
If sliding friction is greater than that of rolling friction, then the wheels cannot move.
Therefore, it is hard to move a bike or a cycle with brakes on.
Moreover, if the brakes are operating perfectly it should be hard to move as their primary function is to prevent the wheels from moving.