The answer to this question has a lot to do with your specific business model. Custom applications are typically for organizations which have a very unique business model. Most companies however can benefit from an off-the-shelf database system that already embraces industry best practices.
The key to determining if you need a custom application is defining your current processes and workflow. This analysis can be done by an experienced IT business consultant. Ideally it will define your current procedures and recommend best practices. If your model is to unique, it might indeed require a custom application design. Otherwise, it might just be a matter of implementing a new system that better adapts to your model.
A hybrid system is also a possibility. In other words, integrating two applications. One of them can be custom or both. At the end of the day, the only true way to know if you need customization is by throughly analyzing your processes and workflow.