Great idea and something that is known as The Precautionary Principle. It is something which the EU and especially Germany has implemented.
Implemented is a big word. It is a principle that exists, but in practice, has been killed by the Lobbying groups. The Dutch Government refused to vote for banning Glycophosphate as a resultt. Same with GenX and other forever chemicals - despite knowing the harm, companies have been permitted to dump them into drinking water reservoirs (!) for decades. All they need to do is come up with one botched study that clears chemical X and you are good to go. Even worse is the permitted use of chemical cocktails, where a dozen of pesticides are mixed, each at the maximum permitted dose and then sprayed onto crops. Just because an individual dose is safe, does not mean that using dozen is. But that is what happens with Strawberries, where they might use between 7 and 17 (!) different pesticides. Anyone with some sense would argue that that might be very unsafe untill proven otherwise, but no... So Precautionary Principle, great on paper, not in practice.
Why would code compiled on your system run any faster than the same code on someone else's system?
Because many pre-compiled packages use conservative optimization flags and may lack specific code paths for certain processors and instruction sets. They might also have chosen a compiler which doesn't produce the fastest code around. I'm not sure how it stands today, but a few years back, ICC produced code up to 30% faster than GCC or MSVC.
The difference all depends on the type of application of course. Overall, you might only see a performance difference of 1-5%, but for specific parts of the application, performance increase may be anywhere between 10 to 200%.
Last, compiling yourself also means you can choose what gets compiled and what not. Which in turns reduces diskspace and memory usage of the executable and may increase security and performance a bit. For things like Kernels and such, you need to compile it yourself if you want support for specific things (ALTQ for PF under FreeBSD for instance).
No police officer is going to give you a ticket for going 5 over the speedlimit so don't even think of using it as an excuse.
Where I live (the Netherlands), below 100km/h there is a 3 km/h correction (3% correction above 100km/h), so driving 54km/h in a 50km/h zone can get you a fine. Granted, a police officer isn't likely to stop you, but driving past a speed trap (which we have a LOT of) is going to land you a ticket.
"The pyramid is opening!" "Which one?" "The one with the ever-widening hole in it!" -- The Firesign Theatre