It could have this result but it doesn't necessarily would have this result. You can justify it either way, depending on your story.

• Say the colony is run along capitalist lines, but every adult has the right to claim a large plot of public land for development. As it happens, the adults at the time of the landing all claimed plots next to each other, in a good place for a capital city (good climate, good transportation, ...). The first hospital, the first university are built there. That makes the initial crew richer than the rest. What is worth more -- a square mile in Manhattan or a square mile in Montana? This could last a long time if the wealth of rich people is self-reinforcing.
• Or the colony does not make the transition away from the shipboard command structure. The captain remains in command until an unspecified time in the future when "the colony is mature enough." Even if promotion to the officer corps is strictly on merit, those raised by officer families would learn how an officer and gentlemen is expected to behave, and hence pass the examination unless they're really stupid. Meanwhile, colonist-born children would have to be really good to overcome that lack of examples.
• Or the crew find that their skills and work culture which where fine on a ship are simply not applicable to the planet. They and the children they raise become an underclass, not a nobility, while they struggle to fit in.

It could have this result but it doesn't necessarily would have this result. You can justify it either way, depending on your story.

• Say the colony is run along capitalist lines, but every adult has the right to claim a large plot of public land for development. As it happens, the adults at the time of the landing all claimed plots next to each other, in a good place for a capital city (good climate, good transportation, ...). The first hospital, the first university are built there. That makes the initial crew richer than the rest. What is worth more -- a square mile in Manhattan or a square mile in Montana? This could last a long time if the wealth of rich people is self-reinforcing.
• Or the colony does not make the transition away from the shipboard command structure. The captain remains in command until an unspecified time in the future when "the colony is mature enough." Even if promotion to the officer corps is strictly on merit, those raised by officer families would learn how an officer and gentlemen is expected to behave, and hence pass the examination unless they're really stupid. Meanwhile, colonist-born children would have to be really good to overcome that lack of examples.
• Or the crew has suffered a high degree of genetic damage due to exposure to radiation and a bit of inbreeding, while the colonists are all carefully selected for health. The descendants of the crew become an underclass.
• Or the crew find that their skills and work culture which where fine on a ship are simply not applicable to the planet. They and the children they raise become an underclass, not a nobility, while they struggle to fit in.

It could have this result but it doesn't necessarily would have this result. You can justify it either way, depending on your story.

• Say the colony is run along capitalist lines, but every adult has the right to claim a large plot of public land for development. As it happens, the adults at the time of the landing all claimed plots next to each other, in a good place for a capital city (good climate, good transportation, ...). The first hospital, the first university are built there. That makes the initial crew richer than the rest. What is worth more -- a square mile in Manhattan or a square mile in Montana? This could last a long time if the wealth of rich people is self-reinforcing.
• Or the crew find that their skills and work culture which where fine on a ship are simply not applicable to the planet. They and the children they raise become an underclass, not a nobility, while they struggle to fit in.

It could have this result but it doesn't necessarily would have this result. You can justify it either way, depending on your story.

• Say the colony is run along capitalist lines, but every adult has the right to claim a large plot of public land for development. As it happens, the adults at the time of the landing all claimed plots next to each other, in a good place for a capital city (good climate, good transportation, ...). The first hospital, the first university are built there. That makes the initial crew richer than the rest. What is worth more -- a square mile in Manhattan or a square mile in Montana? This could last a long time if the wealth of rich people is self-reinforcing.
• Or the colony does not make the transition away from the shipboard command structure. The captain remains in command until an unspecified time in the future when "the colony is mature enough." Even if promotion to the officer corps is strictly on merit, those raised by officer families would learn how an officer and gentlemen is expected to behave, and hence pass the examination unless they're really stupid. Meanwhile, colonist-born children would have to be really good to overcome that lack of examples.
• Or the crew find that their skills and work culture which where fine on a ship are simply not applicable to the planet. They and the children they raise become an underclass, not a nobility, while they struggle to fit in.