1. I never said heat would break the lamp itself. I said that heat can fry the circuitry in the base of a CFL. The fact that you've never observed early failure from CFL heat death doesn't mean it doesn't occur. The Energy Star website agrees with me that this is a problem with at least some CFLs. There's your citation.
2. I certainly did not intend to imply that LEDs could not be used in refrigerators. I intended for the refrigerator part to be just about CFLs and for the oven part to be about both CFLs and LEDs. Sorry if that wasn't clear. The epoxy shell of LEDs would almost certainly melt in ovens (Epoxy apparently melts at about 375 degrees F), and although a fluorescent tube might survive, provided the ballast were located elsewhere, such an installation would require significant modifications to the oven, making it impractical to eliminate this use for the foreseeable future. And of course, when it comes to refrigerators, fluorescent tubes don't appreciate extreme cold, though LEDs could conceivably be used there, provided that the rapid temperature swings when they come on don't cause the solder joints to crack too quickly. I'd probably want to do some experimentation before I said LEDs would be fine there, but it's quite possible that they'd be fine.
3. LED-based bicycle lights and flashlights are a largely unrelated subject. These devices do not use any voltage conversion except possibly a current limiting resistor in series with the LED. The parts that are problematic in terms of requiring adequate ventilation don't exist in those devices because you're starting with DC instead of AC.
4. The failure mode of CFLs dimming is just one of several failure modes that these bulbs can exhibit. Other failure modes include the flicker of death (when the tube won't quite come on) and the electrolytic big bang (where the capacitor in the charge pump blow and the light fails to illuminate entirely). I don't have any statistics on the frequency of these failure modes. It would be an interesting bit of information to have. You know, now that I think about it, it might not be possible to get the flicker of death with CFLs because of the way their ballasts are designed. So it may just be the two failure modes---fading in brightness or suddenly going dead (or fading in brightness and then suddenly going dead).
5. I'm assuming when you said that your lights don't contain electrolytic capacitors, you meant that you spent more money to use film or ceramic caps instead. Unfortunately, most mass-produced devices use mostly electrolytic caps whenever they can because they are cheaper. Expecting your design decisions to be the norm is like expecting people not to eat.
If you don't use any capacitors at all, then how precisely to you generate anything approaching filtered DC without capacitors? And if you say that you use a full wave bridge without any smoothing caps like those @$&% LED Christmas lights that flicker obnoxiously as the light pulsing interacts with the facets on the bulb, I'm going to have to hurt you. :-D