I wouldn't really consider 4 appearances across 7 season "a lot."
For TNG it was.
It's as many appearances as Nechayev got, & she was the most prevalent admiral on the entire show
Over all, it's a fair assumption, given the 3 actual encounters they had with him, two of which involved Romulans crossing into Federation space & the 3rd involving the Devron system in the Neutral Zone itself
I often ponder the scheme they had laid out for Jarok, & consider that as much as it was a test of a potential traitor's loyalty, it was more likely that they knew he was soft already, & played him not as a test, but as a way to use him to provoke conflict
It could also have been tailored by Tamalok himself, to specifically draw Starfleet (& hopefully the Ent-D) into the Neutral Zone, in an attempt to level the political playing field, for the embarrassment of having been caught by Picard at Galorndon Core, only months or maybe weeks before
I totally got the impression that because Picard had diplomatically maneuvered himself out of conflict after letting a Romulan die aboard his ship, caught Tomalak in a lie & then returned the surviving Romulan, in good faith, the whole thing was like a giant slap in Tomalak's face, that he was powerless to combat rightfully
He would have had a lot of finagling to do to regain some of that credibility he'd lost in that encounter, (As it might have even been a mission sanctioned by him) like probably executing that poor SOB that Geordi saved, after a long imprisonment & interrogation,
But more importantly, he'd have to restore his reputation somehow, & a plot that got Starfleet to breach the Neutral Zone would definitely level the playing field, & also make the failed mission to the Galorndon Core somewhat excusable, because it could make the mission's intent look necessary ("We have to send in ships & spies, because they are too")
These were the kinds of things that really made me sit up & take notice of the show's improved quality in season 3