Why are magnetic headings used for designating runways?
There are two parts to the question:

Why number runways based on their direction?

The runways have to be identified somehow and the identification has to be directional. So the, rounded, heading offers itself and it has advantage that:


The pilot can verify they are approaching the intended runway by looking at the compass, which


works at night, in bad visibility or early on the approach when the numbers on the ground are not visible yet and
serves as cross-check for verifying the instruments are set correctly during instrument approaches.

Since the pilot needs to know the runway heading for navigation and for checking the wind anyway, it makes it easier to remember.


Why use magnetic heading instead of true?

In the early days of aviation, magnetic compass was the only tool available for determining direction. It is simple and reliable and well tested in naval navigation. So magnetic headings became the obvious standard.

Later gyrocompass was introduced to overcome the limitation of magnetic compass that it is biased in turns and requires some time to stabilize. However gyrocompass precesses, so it has to be periodically corrected, which was, and is, still done by reference to the magnetic compass.

On the other hand GPS is still a rather recent technology. It is only precise enough to determine heading (or rather tracking) for last 15 years. It requires a complex electronic device that can fail in a myriad of ways and it is affected by many external factors including the state of ionosphere and the selective availability not being turned on again.

And not all aircraft have GPS anyway. So if you wanted to switch the ones that use GPS to true headings, there would still be some that would need to use the magnetic and it would be a mess. On the other hand when you have GPS, you have a computer already and it can contain and use the magnetic declination tables to give you magnetic heading as well.