I don't think we've actually recommended against antivirals for ghsv1, because that's a personal decision. However, ghsv1 sheds at rates that antivirals won't necessarily make a big difference.
We know that ghsv1 sheds a lot less than ohsv1. Oral hsv1 sheds about 25% of days on average (it depends on how often you get outbreaks, how long you've had the infection, etc.), and ghsv1 sheds about 13.7% for the first 3 months, then drops to 7%, and then at 2 years, it drops to 1%.
It also recurs a lot less frequently. 88% of those who, in the first year of infection, don't get an outbreak after their initial one, won't ever get another. Those who do average 1 outbreak a year. Ghsv2 averages 4-5 a year.
Because of all of the above, ghsv1 is virtually non-transmittable in the absence of symptoms. Most experts have never seen it happen. Terri Warren, who runs the Westover Heights site, and wrote the Herpes Handbook, says she hasn't ever seen anyone with a new ghsv1 infection who hasn't received oral sex within the prior two week period.
Also, if a partner already has hsv1, as 2/3 of adults globally do, they can't transmit it to them.
But some people take antivirals for peace of mind, or to appease a partner. If they are a person who does get outbreaks, they may take it to reduce the frequency.
We have no studies to determine if they reduce the shedding at the same rate as they do for ghsv2, but it's generally assumed they work the same way.