>I have seen an (anecdotal) large amount of capacitors failing in consumer televisions. I recently replaced one in a friend's TV. These capacitors are supposed to have rated lifetimes of roughly the lifetime of the TV, so why are they failing in normal use?

The point IMHO revolves around "What is the expected lifetime of a TV (nowadays)?"

More anecdata, I own a "large" 32" Sony Trinitron that is incredibly heavy and that works just fine (touch wood) since 2002 or so.

I also had a smaller Mivar that lasted more than 30 years (if I recall correctly 32 years 1984-2016).

More recently (like 2013 or 2014) I procured for a friend's project a number (20) of (admittedly el-cheapo) Hi-Sense 32" LCD's, 3 or 4 failed in about 25 months (or one month beyond the 24 months covered by warranty) and 2 failed within warranty period (but the importer/assistance center closed before that anyway), of these most were capacitors related issues (one was simply a cold solder joint). But - besides the repaired ones - the remaining 13 or 14 still work just fine.