At no point does the definition of pimp require the person to force the sex worker to do anything.

"Pimp" has specific meaning in the US which criminalizes prostitution:

https://courses2.cit.cornell.edu/sociallaw/student_projects/PimpsandProstitutes.htm

A prostitute is defined as one who exchanges sexual favors for money, drugs, or other desirable commodities, while a pimp is one who controls the actions and lives off the proceeds of one or more prostitutes (Williamson & Cluse-Tolar, 2002; Dalla, 2002). Pimp-controlled prostitution is ubiquitous and the most common form of prostitution in the US by many estimates; the WHISPER organization found 90% of prostituted women they interview are pimp-controlled, Williamson and Cluse-Tolar (2002) estimate that 80% of prostitutes become involved with pimps over time

https://bridgelegal.org/what-is-pimp-legal-definitions-criminal-implications/

In American law, the term pimp refers to individuals who profit from the prostitution of others by coordinating or managing sexual services, often involving coercion, exploitation, or manipulation. Legal definitions vary by state, but common elements include deriving a financial benefit, organizing or controlling a sex worker, and facilitating prostitution.

Common Sex Trafficking Language

Exit Fee — The money a pimp will demand from a victim who is thinking about trying to leave. It will be an exorbitant sum, to discourage her from leaving. Most pimps never let their victims leave freely.

Finesse Pimp/Romeo Pimp — One who prides himself on controlling others primarily through psychological manip­ulation. Although he may shower his victims with affection and gifts (especially during the recruitment phase), the threat of violence is always present.

Gorilla (or Guerilla) Pimp — A pimp who controls his victims almost entirely through physical violence and force.

“John” (a/k/a Buyer or “Trick”) — An individual who pays for or trades something of value for sexual acts.

Kiddie Stroll – An area known for prostitution that features younger victims.