Keep in mind that all electronics do come with a sufficient warranty period. If something is likely to go wrong with the item, it will go in the first 1-3 years and usually covered by warranty. If it does break down in 4-7 years (the usual PSP warranty coverage), is it really worth the extra dollars?
Consider a TV worth $1000. In 5 years, it'll be worth roughly less than half of that, $400. Now, a PSP for that TV will run you about $250-300.
If something does go wrong after the initial warranty period, you will have paid $250-300 to fix something only worth $400. Personally, i'd take that money and use it towards a new TV or a private repair company. If the repairs cost more than what I would have paid for the PSP, i'd rather scrap it and buy myself a current version, newer features and all the good ish, rather than meddle with an aging set.