I would first ask what problem/issue you're solving by combining two cubes into one. Cubes are often split for specific reasons.
Assuming there's no changing your mind to combine the cubes, it's not necessary to start with a new application to accomplish this.
Reason for having these two separate cubes is no longer valid - Part of our company spun off. Right now, having the two separate cubes creates a lot of duplication of work. There are other things we need to update due to the spin off, such as the name of the cubes. What would you suggest?
Without knowing specifics, I would explore creating a summary cube that extends to each of the existing base cubes. I can't say for certain that it would work as you would need to change each of the base cubes Is Top Level Cube for WF property to False and it may not let you.
Alternatively, you could create this linked cube structure (with new cube names) in the existing application (or new one if you prefer a fresh start). This decision is more a matter of preference.
Data-wise it's a wash - you can write a BR to pull data from the legacy application regardless of if it's in the existing or new application.
The main benefit of a new app is that it won't have any remaining "old stuff". However, if you plan on bringing everything into a new app except data, then you're not realizing the benefit. On the other hand, building everything in the existing app may hinder the naming elements because they already exist.