I have a tire recently replaced due to nail too close to side wall, and luckily I have road hazardous warranty on all tires I purchased.. And with that being said, I just patched my brother's tire yesterday the old fashioned way, 1.) because COVID-19, we don't want to take it in. And 2.) my brother isn't in the best of finical situation and we happened to have a patch kit... I've patched many tires in my day and never had a problem with any of them, but I won't say it never will just to be fair because not all repairs is 100% safe, tire shop or self repair.. Posted via the PriusChat mobile app.
(*) That is why we now have TPMS -- to alert the driver to leaks such as that before it gets down so far that the tire overheats and catastrophically fails. (*) In your cars without a spare, you also don't want to find yourself in a situation where you don't have a plug or other DIY flat-repair system and don't have cell reception to call for help.
The reason the screws tend to go into the outer areas of the tires is quite simple. It involves aerodynamics. As a tire rolls along, the treads are made to "suck" at the pavement, therefore keeping tire on the road. Over the years, the computer designs for treads has gotten so good that they suck up debris into the treads and at the very last second, the screw is blasted away from the center of the tire. This was told to me by a tire specialist a few years back. This was when I had very expensive rims and tires on my car and kept picking up nails and screws.
Never mind that those "very expensive" tires probably were soft and thin. Tires don't "suck". That is exactly the opposite of what you want in the rain. Just because somebody puts up a good sounding front doesn't necessarily mean that he really knows anything.