To be fair, Obama didn’t say it this publicly but he also didn’t close Guantanamo Bay or persue any kind of prosecution for the torturers.
Obama was a constitutional law professor and was very serious about following written and unwritten constitutional norms. The problem with Guantanamo Bay, as I understand it, was that they would have had to transfer the prisoners back to a U.S. prison, which would have raised intractable legal issues – they weren’t prisoners of war, but many of them weren’t really charged with criminal charges either. On top of that, some of them were very nasty pieces of work and Obama would suddenly have had full access to the classified material explaining why they were being held, with constant pleas from military and intelligence officers to not release them. That was a fight that he was never going to win.
The problem with trying to prosecute the “enhanced interrogators” was that they were mostly following orders that had been signed off by lawyers. Some of the worst offenders were prosecuted when they started going freelance, but the Bush administration got legal rulings saying that it wasn’t torture. Although it was a new administration under Obama, standard procedure is that administrations continue supporting the legal positions adopted by the lawyers for previous administrations (in other words, the U.S. Government never admits it was wrong). In practice, they change policy and may advocate for changes in the law, but they generally don’t come out and say that previous legal advice was incorrect.
On top of that, if you start prosecuting your own people for following orders, morale will collapse. A quiet change of policy and warning everyone not to do it again is about as much as you can realistically hope for.
Trump assumed he could just walk into office and change policies on a whim, but mostly found himself entangled in a legal and bureaucratic quagmire and he really got very little done. The U.S. government is an enormous beast and getting anything to chance is a monumental task. Dick Cheney was a very experienced bureaucrat and he know how to go about getting what he wanted. Donald Trump didn’t.