It wouldn't have remained that way, Saddam's position was becoming less tenable as time went on, if he had fallen without being pushed, Iran would have been perfectly positioned to gain control either directly or indirectly of Iraq.
Had Saddam had been allowed to remain in power, he would have either left a vacuum into which Iranian supporters would have moved or we would have either a failed state without the coalition troops and resources to combat it or an extension of Iran. Neither was conscionable at the time by either the West or the Arab countries such as Saudi and Kuwait. Having a Somalia in the Middle East is not in our interest.
To state Saddam posed no risk to either the region or to his own people if he remained in power is rather short sighted given his history. If we had managed the situation after his removal better then we almost certainly would not be having this discussion, Iraq would be a viable and hopefully democratic independent stable state and the Arab world wouldn't see the US as aggressors, but partners.
Bush/Rumsfeld were idiots and need to be held to account, not for invasion itself, but the litany of disaster afterward.