1. SDH can also provide you carrier class service, IP over DWDM is right choice if you have too many wavelengths from one point to another (not sub wavelength). You reduce your cost as removing layers.
SDH is right choice when you need subwavelngth kind of capacity between nodes as DWDM crossconnect are not as good as SDH crossconnect.
2. Why router because you are removing the SDH layer.
3. Apart from saving SDH boxes IP over DWDM also will be less complex in troubleshooting. If your router is working fine then problem is in DWDM layer. If you have IP/SDH/DWDM then it is comples to isolate problem.
I think IP over DWDM are still in early stages as is rigid kind of network even with today WXC. Need a totally different kind of wavelength crossconnect to see all the benfits of IP over DWDM.