That's true - current anti-herpes drugs can't eradicate the virus. Even so, there's evidence that the use of anti-herpes drugs could lower the risk of dementia, although to a lesser effect size than the shingles vaccine.

But scientists have also questioned the practicality of using anti-herpes drugs to curb dementia because, as you pointed out, HSV-1 can still reactivate when the drug is discontinued.