What I mean is, if you're using 3, you're approximating, heavily. If you do anything critical using that value, it's as bad as using 5 really, imo. Is it really the case that 3 can be used casually? Like in what, workmanship, crafting or something else?

Personally, I would say that pi should be presented as 3.14 and calculators should be used, there's no reason to fear less than elegant numbers xD. And no, that's not close enough for most engineering work, as an engineer we don't usually approximate that much despite the memes, since you have to reduce the margin of error as much as practical. You generally don't even approximate, just leave it as pi the symbol for the most part since in the end you won't calculate it manually. The errors stack up the more you use the value. Eg, multiply an inaccurate value of pi by pi and the error you get is exponential.

That aside, I think 5 is more elegant than 3 so if youre approximating to avoid the cumbersome numbers why not go for elegance instead of accuracy? xD