This is a pretty common omission to make, even though it's strictly speaking wrong. But suppose for a moment that the algorithm was always fast. In that case, it would not need randomness anymore, as you could just pick a fixed string as the "random" outcome, and you would be guaranteed success. So, if an algorithm uses randomness, it will either fail with some probability or be slow with some probability. If neither is true, that algorithm doesn't need the randomness.

Makes sense. Thank you for the thoughtful response. I hope my original comment is not too misleading.