Your explanation is plausible, but people early in their career are always short of money, with or without student loans:
Need to save a large down payment to buy a home => Better to move to the city where I can save more $$ each year
Need to pay down a large student debt => Better to move to the city where I can pay down more $$ of my debt each year
I'm not disagreeing with you: student debts make the hole larger, so strengthen the effect. But the effect is large in any case (due to most of us being born with a 'short position' on housing).
Need to save a large down payment to buy a home => Better to move to the city where I can save more $$ each year
Need to pay down a large student debt => Better to move to the city where I can pay down more $$ of my debt each year
I'm not disagreeing with you: student debts make the hole larger, so strengthen the effect. But the effect is large in any case (due to most of us being born with a 'short position' on housing).