Yep. And he had other influential protectors in the SS -
Gottlob Berger and
Erich von dem Bach-Zelewski. Alas, neither of these scumbags experienced actual consequences for their crimes. So I doubt they would've gotten rid of him as long as he continued doing as he was told. They would've found more than enough work for him committing atrocities in the East. And the Nazis weren't in the habit of purging their own gang. They certainly wouldn't do it because a Nazi was too evil. Mengele also wasn't regarded as an odious quack by his peers.
Frankly, I'm inclined to take these 'even were totally disgusted by [insert horrible Nazi scumbag] because he was so evil an creepy and we wanted to get rid of him but couldn't' testimonies with a grain of salt. Not saying they're always untrue, but often it comes down to one Nazi trying to whitewash himself when it was convenient for him to do so. After the war, Speer downplayed his interactions with Himmler and portrayed their relationship as antagonistic, when in fact they'd been partners even before the war, when one needed stone and forced labourers for his building projects (the whole point of which was to glorify National Socialism and curry favour with Hitler) and the other needed a way to make his concentration camps economically useful and justify their expansion at a time when all organised political opposition had been crushed.