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not being adequately heatsinked
Well, they have internal short-circuit current limit, plus internal thermal overload protection, plus SOA (safe operating area) protection. Letting them get hot can shorten their life somewhat, but not end it quickly. I've seen them just shut themselves down, and in fact oscillate between on and off because turning off makes the die cool, which again turns it back on, and so on, with some hysteresis. As for how hot a semiconductor can work though, I have had transistors operating under an infra-red microscope to take the temperature of any spot 0.001" diameter, and actually seen them
operate at over 350°C, about 200°C above the maximum at the end of the specified derating curve. I didn't try to see how long they would live at that temperature, but I suspect it would not be much over an hour. At the temperature the 7805 (or better, the LM340T-5) shuts itself down though, I don't think you'll outlive it.
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and then there's all that heat next to an electrolytic cap..
There's no need to have an electrolytic capacitor close to it. Tiny monolithic ceramic ones are good to have close to it though.
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It's also the 21st Century, you don't need to waste watts of electricity for a milliwatt mcu..
Switching regulators don't do well with light loads. They go into pulse-skipping mode and make a lot of electrical noise. Many of them cannot regulate at all at less than 10% of their maximum rated output current. But for a milliwatt MCU, let's say you only need 2mA for the entire computer (like one I mentioned making for a product in the 1980's), and you have a 9V battery to power it (which we also did). I used a linear LM2950 LDO for that one in a TO-92 package (the same kind you see 2N3904 transistors in). If the battery is at 7V, the power dissipation of the linear regulator is (7-5)V*(2+.05)mA=4.1mW. There's a place for switching regulators, but there's still a place for linears. I use both.
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Linear semis also have a significant piracy problem, in that it's good practice now to just test any of their devices you have for being on-spec.
There we buy from reputable distributors who get the product direct from the manuafacturer, so there's no chance someone sneaked in some fakes. If there's a chance of fakes, you might get it from Jameco (which probably sells mostly to hobbyists) but not Mouser or Digi-Key or any of the major industry suppliers. I buy from Jameco sometimes, and have put some Jameco links in, and have not had any trouble; but I would never buy our production parts from them.