Why doesn't civil navigation equipment support TACAN?
Civilian aircraft can use part of TACAN, the Distance Measuring Equipment (DME) signal is the same as civilian DME. As for the directional component one big reason is that the military don't want you to. 

Even if the military didn't mind there would likely be no demand as the costs of using TACANs outweigh the benefits. TACAN is essentially a more accurate version of VOR, and although the complexity and weight of the system has reduced the antenna is still apparently 100 pounds (45kg). For light aircraft that's a fair chunk of useful weight taken off. Cost-wise a VOR setup will set you back somewhere around \$6000 just for the equipment, call it closer to $8000 installed (roughly). A TACAN is a more sophisticated system which would cost a great deal more, say finger in the air of \$20,000, maybe more. TACAN antennas would need to be certified for every single airplane model, and that's going to add to the costs. 

So for a light aircraft I'm going to lose usable weight to an antenna that is also going to throw off my weight and balance, and that's going to cost me at least \$20k when all the equipment, installation and recertification costs are factored in. That's big cash when I already have VOR, ILS, DME, NDB and 3+ satellite navigation systems already available. Oh, and I can also call up ATC most places and say 'help!' if it all goes wrong. There's just no benefit. My phone can tell me where I am if every system on the airplane fails as it has a built in GPS!

For commercial large airplanes it's the same situation. In addition to all the above most will have redundant inertial navigation systems, so even less need for it.