Sure, you could invent a different standard, but what are you going to write into it? "If you input 0.1 into atan, the result should round up when outputting 5

Sure, you could invent a different standard, but what are you going to write into it? "If you input 0.1 into atan, the result should round up when outputting 5 digits, down with 8 digits and up with 12 digits"? Also, "round up" is not any easier than "round correctly" if you require it to be consistent. Say you compute a result like 9.004 and want to round to two digits - if the exact result would have been 8.991, then rounding your computation as 9.01 is different from the standard-specified result of 9.00. So your standard would literally have to specify the desired output for every combination of operation, input, and output precision - obviously impossible.