Yeah that is normally where you install your edge router - at the edge ;) If you also want to use it as internal or core router that is fine too, etc. You can have more than 1 router in a network...
Unless your really worried about complicated firewall rules between your locations/networks routing of traffic can just be done on your L3 switches..
If your looking to replace hardware in your setup - this is perfect time to evaluated that overall design, and does it make sense... Maybe it made sense when it was done, or maybe shortcuts were taken at the time... Or maybe the guy doing it at the time didn't have a freaking clue... But trying to maintain some setup, just because that is the way it was setup before you is not a good plan..
Look at the details of the network, what talks to what, how much bandwidth is available and or used, etc. What hardware you have to work with.. Or what budget you have to replace, uplift aging hardware, etc.
What I can see from just your original drawing - is does not seem optimal at all.. Now maybe you drew it wrong, maybe you left out details and works different than it looks? But my gut reaction to that drawing is its borked..