I assume Linux's software RAID is as reliable as a hardware RAID card without a BBU and with write-back caching enabled. After all, uncommitted data in a software RAID system resides in the kernel's buffer cache, which is a form of write-back caching without battery backup.
Since every hardware RAID-5 card I have ever used allows you to enable write-back caching without having a BBU, I expect software RAID-5 can work okay for people with a certain level of risk tolerance.
That having been said, I have personally experienced serious data loss due to having no BBU installed on a RAID-5 card though write-back caching was enabled. (No UPS, either. Don't yell at me, not my call.)
My boss called me in a panic while I was on vacation because one of our production systems wouldn't come back up after a power outage. He'd run out of things to try. I had to pull off to the side of the road, pull out the laptop, turn on WiFi tethering on my phone,
ssh into the stricken system, and fix it, while my family sat there with me on the side of the road until I finished restoring a roached database table from backup. (We were about a mile away from losing cell reception at the time.)
So tell me: how much would you pay for a RAID card + BBU now?