[kapital]

Why are signal of deuterated solvents not seen on H-NMR, while they are(?) NMR active(based on the fact that they do couple with protons)?

[Corribus]

Deuterium peaks are not observed in an ¹H NMR spectrum because ²H resonates at a very different frequency than ¹H. ¹H does couple to ²H but the coupling constant is incredibly small (I looked around and it seems the J_HH and J_HD values are around a ratio of 1 to 6; another value I found puts it at about 0.01-0.02 ppm). So, I guess if your resolution is good enough you could see it. As I understand, if you deliberately deuterate specific positions in a complex molecule, the resonances of the deuterated positions in the proton NMR spectrum will disappear, and the resonances of protons adjacent to the deuterated position will slightly broaden. The broadening is due to J_HD. (See, for example, Figure 7.2.7 here.)

[Babcock_Hall]

One source I consulted some time ago suggested that the ratio of the two kinds of coupling constants was the same as the ratio of gyromagnetic values of the two nuclei, which is about 1/6.5.  When I have measured ²J_HD values, they fall around 2-3 Hz (roughly speaking), which is in the expected range for geminal coupling.  The same holds true for one-bond carbon/deuterium coupling constants that I have looked at (not systematically).
EDT
We do see the deuterium in NMR, every time we look at the lock channel.