Altitudes flown aren't independent of heading. Depending on whether you are VFR, IFR, flying magnetic east or west, you will fly at specified 500 foot increments.

https://www.law.cornell.edu/cfr/text/14/91.159

Edit: I read up a little more about the accident, and it happened above where these rules apply. In any case, with problems like this where one plane isn't where it should be, I think the solution is to come up with better ways of ensuring clearances are complied with, not coming up with a system that is more tolerant of people violating clearances. Airspace is only going to get more congested and the only way do accommodate that safely is to have planes follow clearances to stricter and stricter tolerances.

Your suggestion would kill GA (general aviation) if you had to fly a specific altitude for a given direction. A good gust and a rusty pilot could rise or fall a couple hundred feet pretty easily. Size of the plane matters a lot too. Plus, what altimeter setting are you using? (What is 2000 ft? AGL? MSL? Pressure altitude?) You would also frequently be required to violate these altitudes to maintain VFR conditions because clouds are moving into your airspace. And how do you do something like circling a point? How do you enter a traffic pattern? You would hit task saturation in no time.

I say this as a math lover (physics degree holding) and a pilot. Currently we have a rule; "Odd pilots fly East", so you could be 3500,5500,7500, etc. Going west at 2500,4500,6500, etc. Everyone should also be using flight following for anything but a really short flight. And flight following is really going to help with collision avoidance.

Presumably this would only apply in class A airspace above 18,000 MSL. No one hand-flies there anyway.

Recommended above 3000’ in all airspaces unless you’re in a pattern or CTA then you follow ATC.

It does not address the altitude issue, but there is https://en.wikipedia.org/wiki/Strategic_lateral_offset_proce... which addresses aircraft on the same route.