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In fact, in my opinion, RAID increases your need to make regular backups because it increases the number of possible failure points related to the data you've stored on it.

I think RAID simply shifts the critical failure point from the disk to the controller. Assuming you don't have any other issues with cooling system. And, I agree its a very questionable idea that a disk will be more likely to fail than a controller. Maybe that's statistically true but... so what? We don't live off statistics, we live off individual specific cases .
Personally, I too am happy with software raid. I had a RAID5 volume, software-based, on Windows 2000 Server. I removed the three IDE disks and installed them into a Windows Server 2003 machine, newer and completely different hardware. The volume was recognized. I am sure Linux does exactly the same.

Certainly I still need backup, but given that I do a periodic backup, software raid adds a significant protection against data loss due to disk failures. Without a software raid, a disk failure would mean loosing all data since last backup, be it 1 hour or 1 month ago. That's enough to make me spend few extra euros on one extra disk.