In short – No.
Any change in employment must be by mutual consent and the employee cannot be coerced to change if they do not wish to.
Often a casual role will be at a higher rate, and while it does forego the leave entitlements, the difference in pay this can be a preference. By changing to part-time, the employee will go onto a lower rate but with the inclusion of leave entitlements.
While this would vary per case, the allure of casual employment comes with the flexibility of hours, even if the role is a long term casual. This can be favoured for those with external and fluctuating commitments, such as families and children.
Some may not wish to change for these reasons and are not required to change.