Actually the meaning of the Ved mantra are produced by rishi who has done hard practice of Yoga philosophy and has studied all Vedas. Because Rigvedamantra 1/164/16 says, "NA CHIKET ANDHSAH" I.E., he who is not a yogi and has not realized God cannot know the real meaning. Within five thousands years the false statement against the Vedas are being spread and people being innocent, accept the false. In Atharvaveda kand 9 sukta 4 it is said that bull must be nursed carefully because he will give the calf to the cow with the result there will be plenty of milk, butter and ghee in your houses. But intentionally the meaning has been changed that while performing Yajna the bull must be slaughtered and its meat should bedistributed. Same case is of Ashwamedh word.
Yask Muni who was philosopher of Vedas and Yoga says in his Shatpath Brahmin Granth 13/1/6, "RASHTRAM WA ASHWAMEDHAH" i.e., meaning of Ashwamedh is Rashtra i.e., nation. So to perform Yajna for the benefit of the nation is called ashwamedhaha and the king who rules over the public and does justice and performs Ashwamedh Yaj, he is true king. So here ashwa means Yajna and not horse. Because there is no place of violence in Yajna.
So purpose to perform Ashwamedh Yaj by a king is to look after his public well and is to give peace and fearless atmosphere. Process is mentioned in the book named, "YAJ KARAM SARVSHRESHTHA ISHWAR POOJA". So dueto wrong/false meaning the public has left the yajna within past two to three thousand years or after Mahabhart war.