Is it reasonable for the company to ask for recruitment fees when leaving the company?

It is completely within the company's internal regulations and is illegal. There is no need to pay any fees for employee applications.

According to the law, the employer shall not detain the employee's identity card and other documents, and shall not require the employee to provide a guarantee or collect property from the employee in other names. Units shall collect tooling fees in accordance with internal regulations, and report to the labor law enforcement and supervision departments in violation of legal provisions.