With software raid, there is no controller to fail.
Well, that’s not strictly true, because you still have a SATA/SAS controller, HBA, backplane, or whatever, but they’re more easily replaceable. (Unless it’s integrated in the motherboard, but then it’s not a separate component to fail.)
This is poorly phrased. A raid with a bad disk is not failed, it is degraded. The entire array is not more likely to fail than a single disk.
Yes, you are more likely to experience a disk failure, but like you said, only because you have more disks in the first place. (However, there is also the phenomenon where, after replacing a failed disk, the additional load during the rebuild might cause a second disk to fail, which is why you should replace failed disks as soon as possible. And have backups.)