There are ways of repeating quantum information that protect against accidental measurement errors. For example, if your logical 0 is |000> + |110> + |011> + |101> and your logical 1 is |111> + |001> + |100> + |010> then can recover from one accidental measurement. And there are more complex states that protect against both bitflip errors and accidental measurements simultaneously. They're just more complicated to describe (and implement!) than "use 0000000 instead of 0 and 1111111 instead of 1".