Probably talking through my rear here, but my understanding was also that vaccines are only effective in those who are not yet infected. Since EBV is for life, you'd never reach a point where you were vulnerable to reinfection and thus could benefit again from vaccination.
It's complex.
The body does not make a robust immune response to all viruses, and a vaccine can greatly help.
Some examples - not all very related.
Rabies virus is pretty much 100% fatal - but a large fraction of people who die from it seem at the end to have antibodies that probably would clear the virus given time - it's just not enough, as by that time it's already gotten into the brain, and they die. If you give vaccine at the start, it lets the immune system kill it before it can get that far, and develop the immune response early enough to cope with minimum or no later problems.
Shingles is caused by a reactivation of the chicken-pox virus that has lain dormant for some years. Immune responses to viruses can decay over time, perhaps combined with the virus mutating to escape the immune response, though due in many cases to immune suppression - either the normal one through age, or other causes. A vaccine is available which boosts the immunity (though you have some natural immunity already because you were infected with chickenpox) and prevents (or greatly reduces the chance of) a reactivation and shingles.
Norovirus (winter vomiting disease) is another example - in this case the immunity made to it is not great, and you can get reinfected by the same strain in a fairly short time.
On EBV, a vaccine could help in several ways. (these are all entirely made up by me, and seem sort-of-plausible)
If flares of EBV activity are triggered by severe stress (including PEM), which causes an immune response which is misdirected in the same way that initially causes CFS, reeducating the immune system with a vaccine, and strengthening it so the immune system is better able to kill the flares promptly, or even eliminate the virus might, if not curing a patients CFS, at least stop the prospect of subsequent activations of the virus causing a significant worsening.
If there are several strains of EBV, it may be possible to be infected again, and get a 'new' response to that infection, because your initial immune response was specific to that strain. A proper vaccine may be able to cover all circulating strains.
If the bodies immune response is not for some reason clearing the infection, but a more robust response could reduce it to a low enough level that whatever it's doing to the immune system on a sustained basis stops, it might be a 'cure'.
In addition, antivirals are unfortunately not in general very widely acting - we're not at the early antibiotic era, when everything died to penicillin.
Viruses mutate much more rapidly - HIV has taught us that you need to use several effective antivirals at once in many cases to control an infection.
EBV may of course differ. But a quick search leads to attempts to clear EBV from people who are voluntary organ donors, which unfortunately failed with common antivirals.
