Incorrect. For starters, acquaint yourself with Melchesidech in the Old Testament and the following Matthew 19:12, 27-30; Luke 18:28-30 and the following from the Second Council of Carthage:
'ut quod apostoli docuerunt, et ipsa servavit antiquitas nos quoque custodiamus'
As for your references (also Mark 10:20-21), as well as from I Corinithians, it is clear that celibacy is held to a higher standard, but leaving one's wife, brother in the words of our Lord, does not imply celibacy is ordained by God. It simply says that placing God first will be rewarded. As to how will we ordinary people faire is a different story -- I can only say that God is merciful and just and whatever He decides for all of us will be merciful and just.
Celibacy became an absolute requirement of the Church in the West. Local (Latin) Councils of Elvira and Carthage (4th century) established celibacy for bishops and priests. Exceptions to the strict celibacy were introduced by the Vatican II (deacons and convert priests), but as far as the RCC is concerned, celibacy is good as dogma.
Which leaves Scriptural permission for priests and bishops to marry (1 Timothy) out in the cold. All other NT references only recommend and praise celibacy but do not make it mandatory. Thus, outlawing celibacy for clergy is contrary to Scriptures and is a local tradition that is open to change.