Daniel Prince wrote:

I have read that electrolytic capacitors are the least reliable
component in power supplies. I have also read that there are
motherboards with solid polymer capacitors. Are there any power
supplies with solid polymer capacitors?

Try the usual places where experts test and disect PSUs (they actually
remove all the power transistors and diodes), like:

www.JonnyGuru.com
www.HardwareSecrets.com
www.HardOCP.com
www.XbitLabs.com

I don' t know if any PC PSUs use polymer/organic/os-con caps
exclusively on the low voltage side (the only place they will be
found, as polymers aren't made for more than about 30-50 volts).
Polymers seem to be found mostly in PSUs with really high power
ratings, but Seasonic makes a 650W with some in it.

More important than having polymers is not having junk brand caps
because junk can fail in just 1-2 years, while good conventional
electrolytics can last a decade, as demonstrated by my vintage 1999
Delta PSUs (only Japanese caps -- none bulging, and the few I sampled
measured in specs for capacitance and ESR last year) and my 33-year-
old TV (only 2 of its Sanyo caps failed, and I love the fake wood
grain).