I see 2 reasons for Liberty to effectively ignore most "civilian" Zoner things in Liberty.
The Order have agents everywhere. They are in every level of Liberty Goverment, the LPI, the LN, and the LSF. The Order has much more effective assets than any Zoner within Liberty and Liberty knows this.
In addition, Liberty has a need for the intel that Zoners regularly provide concerning every House and Fringe system in Sirus. Moreoever, every "spy" agency of every house and faction in Sirus regularly uses the Zoner Freeport network as well as the "Zoner" tag affiliation for an endless number of official, non-official, espionage, political, and economic reasons. These uses, to me at least, are a large part of the power and influence FL lore alludes to about Zoners, without being specific.