To me, it's more to do with the software.
Not the software but the overall system. However, that has very little to do with whether the write back cache is enabled or not on the RAID card.
The battery backup on the RAID card is there for two reasons.
1. With a write back cache the card can "lie" to the host about whether have written a data block to disk. Hard drives and their caches can have same issue. Most don't have a battery or capacitor to cover up that lie if power disappears suddenly so in a safe oriented configuration that is turned off.
A write back cache on a RAID card isn't going to do much if there are moderate frequency of large (i.e., write sequences at least as large as the cache) bundles of data. (e.g., writing 500MB files when the cache is 100MB. )
2. For RAID 5 and 6 there are multiple read/write/write operations to be done to disk that should be done atomic but may not be if power fails. That's not data from the host that is data the RAID card is composing for its "magic". That isn't a write cache.
The reason why need UPS in these two cases is because the battery only protects the memory. What needs to happen is more disks writes so that the card can get rid of this transient state. Some new RAID cards have Flash storage on board so they can write this temporarily to flash even if the disks aren't around. But has to get written somewhere.
There are other "half completed" stuff in the OS and Apps too. However, a "clean" shutdown would be good if there was no RAID card at all. If you just had regular disks on a simple internal SATA controller it would be less messy to just do a shutdown once power goes away. Nothing particularly unique to the RAID card's caches are present in that issue.
Brown outs ... that is just crappy power. The RAID card isn't alone is being better off if don't feed it crappy power. Hardly any electrical element in the whole system wants to eat crappy power.