They would with me (My actual first name is Edwin) because I served on a board of trustees set up to rewrite the manual for sex workers anonymous in the years 2013, 2014, and 2015.
Forced prostitution generates a supply to meet a demand.
A significant part of the demand is always youth. Everything from just under the age of consent, to infants. So outside of India and the Islamic world that is always illegal and the people who fall prey to that very often continue as adults or return to prostitution as adults.
The people who desire to purchase the young do not settle for older prostitutes just because it becomes legal someplace. They will risk prison to buy what they want. Hell, they will travel across the planet and risk miserable foreign prisons.
Agreed, legalizing prostitution by adults leaves child trafficking untouched. As you indicate, they're separate issues.