Of course it makes sense.
Academia, like many other fields, is strongly influenced by networks and connections. It’s all about who you know, and who you’ve worked with. Having broad networks only benefits aspiring scholars, and most serious graduate students are encouraged to start expanding that network in their first year.
Attending a graduate program outside of your own undergraduate department not only connects you to people you don’t already know; it also exposes you to different philosophies and approaches. This is especially important in a social science field like economics, where approach and philosophy have a big influence on how economists go about doing their work.
Sometimes it makes sense to go to your undergraduate department - they may just be the best department, or one of the best, in the student’s interest/specialty area.
Columbia does have a standalone economics master’s program: https://econ.columbia.edu/masters/