Elimelech's Son Obed?

In Duet. 25:5-10, provision is made to continue a dead brother's name if he has no sons, by his brother marrying his wife and having sons for him in his place.

This occurred with Boaz marrying Ruth to perpetuate the clan of Elimelech as indicated below in Ruth 4:10:

10 "Moreover Ruth the Moabitess, the wife of Mahlon, have I purchased to be my wife, to raise up the name of the dead upon his inheritance, that the name of the dead be not cut off from among his brethren, and from the gate of his place: ye are witnesses this day."

So Obed was born to Boaz and Ruth, to be Mahlon's son to perpetate Elimelech's clan.

Yet in Ruth 4:21 (and in Matthew and Luke), Obed is listed as the son of Boaz as though Elimelech never existed.

Should Obed be considered the son of Boaz when Boaz was a substitute for Elimelech (or his son Mahlon) in being the father of Obed? If so, why?