How important are redundant power supplies in servers, not measured by how critical server uptime is, but by likelihood of failure?
In other words, are server PSU's error prone and/or likely to fail within the first 3-4 years of service?
I had a warranty PSU exchange in maybe 30% of my devices over the years. I consider this high enough that I want redundancy for this and would recommend it wherever feasible. In fact, PSUs were the only part except HDs I ever had to replace.
There are other reasons to consider redundant power as well:
One advanced feature available on high-end machines (especially servers) but also available to the general public for those willing to pay for it, is a redundant power supply . In essence, this is a power supply that actually includes two (or more) units within it, each of which is capable of powering the entire system by itself. If for some reason there is a failure in one of the units, the other one will seamlessly take over to prevent the loss of power to the PC. You can usually even replace the damaged unit without taking the machine down. This is called hot swapping, and is an essential productivity backup for use in servers and other machines used by a number of people.
Redundant power supplies are commonly used in conjunction with RAID arrays in systems requiring a high degree of fault tolerance.
I think if you have multiple servers running (active-passive or load balancing mode), you don't need to worry about redundant power supplies. Running another identical server is better (in terms of availability) than having a complete redundant single server.
At the same time, it is recommended to have redundancy for your data using RAID.
Honestly, you're probably more like than not to have no issues with a single power supply over a span of 3-4 years.
That said, the power supply is one of the more likely pieces to fail in a server. Adding redundancy here is relatively cheap insurance against a failure. Having to order a replacement or drive out to get one can be a painful experience that one wouldn't like to repeat.