Worried is one thing, but when he gets worried, he goes to check it out. He doesn't start plotting to undermine Rand in areas well outside his wheelhouse, or demand a guy with AoL knowledge and ta'veren pulls justify his plans to a teenager with only the most cursory training in fallen modern techniques, and whose only claim to importance is based on a farcical ascent through ranks of an organization neither he nor anyone else from their home holds on much respect.
All Egwene is doing is attempting to interfere with what he needs to do to beat the Dark One. Freedom isn't worth much when they try to take your raison d'etre off the table.
So by your own admission, it,s all about what Egwene or the Tower wants, and the hell with what Rand needs to unify humanity or defeat the Dark One.

All of that is stuff Egwene has no way of knowing about, and completely unsupported by his actual behavior in the Tower. Meanwhile she had no interest in anything like close observation or moral guidance when she was with him. Once her hero As Sedai was gone and sucking up to his advisor was no longer a motive, she kept away from him except when she wanted something, for herself or the As Sedai faction she had engaged in a long distance romance, and for which she fully intended to betray even the confidences and trust of her boyfriend & intended.
Mostly Egwene just objected to stuff like his intention to kill one of the Forsaken who had openly seized the throne of a powerful nation, or commanding his troops to refrain from rapine, pillage and genocide under the traditional penalty of death, or getting some mutual nookie from a really gorgeous woman who has proven herself at this point to be his most loyal and capable subordinate monarch. so much for her judgement of character.