Hare Krsna,
It is an important point to consider why Kardama Muni desired to leave home to seek self-realization rather than stay at home and associate with His son Kapiladeva directly. It is clear that devotional service has different flavors and moods. While I am not competent to understand what went into the mind of Kardama Muni, I can share my own realizations.
The first reason could be that Kardama Muni desired to follow his own natural propensity, his sva-dharma. Kardama Muni used to be a strict brahmacari and a yogi. It is mentioned that he meditated in yoga for ten thousand years before attaining perfection. He attained success, and the Lord, being pleased with him, showed him His form. This proves that he attained perfection in yoga practice or meditation by satisfying the Supreme Personality of Godhead. He actually saw the eternal, blissful and transcendental form of the Lord.
“Kardama Muni saw the Supreme Personality of Godhead, who is free from material contamination, in His eternal form, effulgent like the sun, wearing a garland of white lotuses and water lilies. The Lord was clad in spotless yellow silk, and His lotus face was fringed with slick dark locks of curly hair…When Kardama Muni actually realized the Supreme Personality of Godhead in person, he was greatly satisfied because his transcendental desire was fulfilled. He fell on the ground with his head bowed to offer obeisances unto the lotus feet of the Lord. His heart naturally full of love of God, with folded hands he satisfied the Lord with prayers.” (SB 3.21.10-12)
This means he already tasted transcendence before his married life. He continued to desire that transcendence even after fulfilling his family responsibilities.
The second reason could be that Kardama Muni, being a self-realized soul, desired to strictly follow the directions of the scriptures. In the scriptures it is recommended that one must leave home after his fiftieth year and thus follow prescribed varnasrama-dharma. He wanted to follow the Vedic injunctions to set an example for others. He married to fulfill the desire of his father, Lord Brahma, who ordered him to enter householder life to beget children and increase progeny for populating the universe. He performed that responsibility obediently and perfectly. Family life has its own challenges and Kardama Muni may have felt that household life may distract him from remembering the Lord constantly. Thus he desired to leave home.
“Today I have something to ask from You, who are the Lord of all living entities. Since I have now been liberated by You from my debts to my father, and since all my desires are fulfilled, I wish to accept the order of an itinerant mendicant. Renouncing this family life, I wish to wander about, free from lamentation, thinking always of You in my heart.” (SB 3.24.34)
The third reason could be that Kardama Muni desired to have his wife Devahuti take full advantage of her son (Lord Kapiladeva) to achieve self-realization. Great souls not only desire their own spiritual upliftment but also wants to give opportunity to others to progress in spiritual life. Kardama Muni saw that Devahuti served him sincerely during their household life together. Due to her responsibility and service to her husband, Devahuti was not able to devote fully to devotional service. Now she wants to work on that missing part of her life. Devahuti said to her husband,
“Until now we have simply wasted so much of our time in sense gratification, neglecting to cultivate knowledge of the Supreme Lord. Not knowing your transcendental situation, I have loved you while remaining attached to the objects of the senses. Nonetheless, let the affinity I have developed for you rid me of all fear. Association for sense gratification is certainly the path of bondage. But the same type of association, performed with a saintly person, leads to the path of liberation, even if performed without knowledge. Anyone whose work is not meant to elevate him to religious life, anyone whose religious ritualistic performances do not raise him to renunciation, and anyone situated in renunciation that does not lead him to devotional service to the Supreme Personality of Godhead, must be considered dead, although he is breathing. My lord, surely I have been solidly cheated by the insurmountable illusory energy of the Supreme Personality of Godhead, for in spite of having obtained your association, which gives liberation from material bondage, I did not seek such liberation.” (SB 3.23.53-57)
Kardama Muni did not want to remain at home and be responsible for depriving his wife of taking complete shelter of her son, Kapiladeva. There is a chance that as long as Kardama Muni stayed at home, Devahuti, being a dutiful wife, would continue to render service to her husband and thus not be able to take full advantage of associating with her son. Thus Kardama Muni may have felt that it is better to leave home and give Devahuti complete opportunity to associate with her son and progress in devotional life. At the same time, he would be able to wander as a mendicant and devote himself completely in remembrance of the Supreme Lord in his heart. This is a win-win situation for both him and his wife Devahuti.
“Today I have something to ask from You, who are the Lord of all living entities. Since I have now been liberated by You from my debts to my father, and since all my desires are fulfilled, I wish to accept the order of an itinerant mendicant. Renouncing this family life, I wish to wander about, free from lamentation, thinking always of You in my heart.” (SB 3.24.34)
These are my own realizations, and I could be wrong.
All glories to Srila Prabhupada!
Krsna Katha 