The operator can only carry a limited amount of ammunition, sustained automatic fire just isn't sustainable in a battle and if you run out then you are useless. Most firing with machine guns was done in short bursts anyway but semi-automatic firing makes it easier to conserve ammunition so they can keep firing for longer.

You can also be more accurate when firing in semi-automatic mode and the MG-34 was quite accurate at range.

Ultimately though it wasn't that useful a feature for the German army since they preferred higher rates of fire for more killing power in short bursts and it was harder to build so they didn't add it to the MG-42.

The intention of a machine gun is to lay down a large amount of fire quickly. Unfortunately that quickness also means increased recoil which often makes the weapon inaccurate.

The use of semi-automatic would allow aimed shots that are much more accurate than a burst. For example if the enemy were reasonably close and visible it might be better to shoot at him with an aimed single shot which is more likely to hit than a burst. This means you'd hit him rather than just keep his head down.