Talented or not, directives toward which a victim is most inclined are always easiest to Compel (unless Moghedien lied to Liandrin, hardly beyond the realm of possibility.) We likewise know Balthamel had SOME talent and skill with Compulsion because we saw him use it at Graendals request. Logically, it was probably not an especially rare or clumsy practice among the Forsaken, who were themselves greatly "inclined" to employ such a powerful tool with no concern for its destructive effects. We know Graendals habit of using it like a sledgehammer drew her associates scorn, but that was simply because she rarely cared enough about the damage to use a lighter touch, not because the AoLs foremost mental health specialist lacked the skill. We also know Balthamel in particular was an infamous lech and sexual deviant/predator (I want to say his crimes were great enough to earn him Severing,) so we have every reason to believe he would have practiced until quite adept with Compulsion. That illustrates another advantage the Forsaken had with Compulsion: Not only were they inclined to use it, with no regard for its harmful effects, but during the century-long War of the Power they acquired countless victims on whom they could experiment and refine their techniques.

If I had to bet, it would not only be that Balthamel used Compulsion on Egwene, but SO skillfully neither she nor we have ever detected any hint of it. It strains the limits of plausibility to believe Balthamel had the means to Compel Egwene and was tasked with controlling her (both of which were stated in the text,) yet never once used the former to aid the latter. The absence of hints would not mean much in itself, because Jordan and Sanderson have the luxury of revealing her PoV and everyone elses selectively. Half of Randland could be convinced she is under Compulsion and we would never know it if the authors deliberately concealed all evidence of it until a time of their choosing.