As I'm familiar with client-side configuration tools for several business oriented commercial router firmwares, pbx systems and switches, I can only strongly recommend against this madness. Infrastructure devices tend to stay around for a long time, even beyond their EOL/ EOS dates - and it's very, very inconvenient having to keep a VM with e.g. Windows XP before SP2 and no security updates around, just to run the configuration program for your ISDN pbx.
The same goes for relying too much on fancy web frameworks of the day, which age very badly (the ie6 dilemma). A router firmware doesn't need to look pretty, it needs to work - and be compatible with ~10 year old browsers, just as well as new browsers 10 years into the future.
And yes, obviously as mentioned before, you definitely can't rely on external services for anything, APIs break, servers go away - and you need administration access to your router most, when the internet isn't working.