/spawnpoint @p ~0 ~0 ~0 not working as expected

While I can see why this is bothering, you can work around this problem like this:
If you want to do /spawnpoint @p ~5 ~-10 ~0

Then do this:
/tp @p ~5 ~-10 ~0
/spawnpoint @p
/tp @p ~-5 ~10 ~0

Doesn't /spawnpoint @p require coordinates to function though?

And your system above would cause unnecessary jittering for the player

Nope! If you only do "/spawnpoint @p", it will set their spawn to their current location.

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

Tails, you can resolve this bug. Execute can handle this type of request now.

Indeed whilst you can execute for spawnpoints, there is a particular issue that executed spawnpoint does not accept relative co-ordinates when run in an execute as detailed in MC-63964.

Yes it does. With execute you can issue a spawnpoint command with relative coordinates.

I fully agree that you can, and whilst the block outputs that it has set the player's spawn to whatever the relative command should be, (at least in the examples I have tested and in versions up to 14w30) when the player is killed thy are returned to worldspawn

If they are returned to the worldspawn, then the spawn wasn't set properly. The game will say that spawnpoint was set even in an obstructed location. Execute @p works fine.