Why do you have to plant seedlings, why can't you just scatter the seed and you're done?
For plants that are cold-tolerant or with a short growing season, it works to just scatter the seeds, sometimes water them and then harvest the crop. Such e.g. radishes, peas, onions, beets, lettuce...
However, light-demanding plants that like a long, warm period, such as peppers and tomatoes (eggplants, melons, etc.), produce very late if they are just sown in their place, without seedlings. In order to have a relatively quick crop, we sow the seeds in time (it's still cold outside) in a sheltered place. When the frost-dangerous period outside has passed - roughly in the middle of May (in Hungary) - we can plant out the relatively larger plants by then.
Of course, you can also buy seedlings, but there is something special about home-grown vegetables. Even children eat more vegetables that they grew and watered themselves.