The point of using a cache is to have data in memory and not on disk. From what I can tell, Postge Unlogged tables are still written to (and read from) disk. It is just that the write is done in an unsafe way.
The article explains how one would go about benchmarking performance but forgets to actually include performance metrics. Luckily they link to another write up that does. Using an Unlogged table vs. a regular table reduces write times about 45% and gives you about 3 times as many transactions per second. It is not nothing but it is probably not worth the code complexity vs. writing directly to a persistent table.
Even the “no persistence” behavior of a cache is not strictly true: an unlogged table is only truncated if Postgre is shut down unexpectedly (by kill -9 the process or by killing the VM). If you restart if you shut down the process in a controlled manner, the unlogged table is properly persisted and still has data when it starts.
I also like checked exceptions. I like having a compile time check that I thought through error scenarios.
Is it perfect? No, but it should be iterated upon, not discarded.
FYI, catching and rethrowing as an unchecked exception is a pretty bad anti-patern (and a foul code smell).