From the business perspective, there is no need for Application Modernization. If they are content with the functionality they currently have, there is no need to fund a modernization project.
Modernization has to be approached from a risk and benefits perspective. IT organizations must identify the risks associated with not modernizing. For example: supporting an application written in an unsupported technology presents a risk to the business if the application fails and cannot be fixed. Another reason to modernize would be to reduce the overall support and operational costs. This is only justifiable if the savings from modernization exceed the cost of modernizing.
Finally, modernization projects must be planned and implemented so they do not impact critical business projects.