Viruses are tough little beggers. Killing them directly is problematic because viruses by their nature hijack your host cells to live and replicate. You'd have to kill off your own cells to kill the viruses directly. That's a risky proposition. Antiviral medications don't kill viruses. They work by inhibiting viral replication (the virus can't spread) and letting your immune system (or normal cell death) take care of the already-infected cells. This is one reason why viruses are especially difficult to manage in people with impaired immune systems -- it takes a long time for the infected cells to all die out if your immune system is not helping the matter along.
I hope you have Valtrex, not Valcyte, for your EBV. Valcyte is a much riskier medication than Valtrex and isn't particularly effective for EBV. If you need Valcyte for HHV6 or CMV, then you have to take the risk because it's better than the infection, but I wouldn't take the risk when there's a less risky, more effective, medication.