That's a cost/benefit choice.

It's why it is recommended to plant in the Fall vs the Spring.

Costs are efforts/work and monetary expenditures. Benefits are the final result.

Seed to soil contact is very important for the newly germinated plant to establish itself in the soil. So, roughing up the soil will remove any ground cover for improved contact. creates furrows for the seed to nestle in and as the furrow collapses over the seed, help moisture retention around the seed.

Topdressing, like the furrows will help maintain moisture around the seed and to a minor extent, keep the seed from floating and relocating due to puddling during a minor rainfall. Topdressing with soil is discouraged as it can change drainage and make for uneven lawns. It can also be very difficult to spread and you don't want to cover the seed with any material in excess of 1/4". Peat MOSS is a better choice.

In a Spring seeding, you are up against two big obstacles. The biggest is the new turf surviving the Summer. Roots grow well when soil temps are between 55 and 65F and although growth to some extent continues until the ground freezes, it stops when temps exceed 75F. Spring seeded grass has very little time to establish root mass before Summer making it susceptible to water and nutrient deficiencies and related stress. Mature grass stores carbohydrates in early summer to help it survive Summer (when heat makes photosynthesis very inefficient) and come out of any Summer Dormancy. New grasses are using carbohydrates in an effort to grow and establish themselves. Many turf diseases occur in late Spring and Summer. New grass blades (like those on young turf) are more susceptible to disease and without stored carbs, the young grass is less able to fight off disease and insect damage. The next big problem is weed pressure. Spring and early Summer is when weeds proliferate. they are designed to out compete other plants for water, nutrients and light. New grass does not compete well.

I Spring overseed, so I don't intend to discourage you from doing it. However, I limit my cost because of the lessened benefits. I just spread seed and what makes it, makes it and I put the real effort into the Fall.