It's easier to protect seedlings form pests because they are concentrated in seedling trays and are mobile, meaning they can be moved to another site if pests are eating the seedlings

Easier to control the soil quality (high quality seed raising mix) and heating/cooling (both with glass/plastic domes) and artificial heating devices.

You can place seedlings precisely where you want them instead on the somewhat hit and miss method of sowing directly into a garden bed.

While a crop in the ground is maturing you can be already growing the next crop in as seedlings.  Once the crop in the ground is harvested and manured you can immediately plant your seedlings that have already had four weeks growth, thus reducing the turnover time (the time from planting through to harvest and then making the bed ready for the next planting) by around four weeks.