Why would you bother taking a trip that involved leaving your entire species hundreds of thousands, even millions of years behind you? It would be energetically expensive, and the civilization that launched it couldn’t expect to care or remember by the time it arrived. That might work for a small group of pioneers willing to go into the blackness, but it’s not the basis for a galactic civilization.

Even though it May not seem logical, the point is that interstellar travel without FTL speed is feasible.

Its possible, but not at all feasible. It’s also not really practical and the nature of it undercuts the usual “where are all of the intelligent species colonizing the galaxy?” arguments which tend to crop up.