Rex wasn't proud of his pain tolerance.
It was something that he was trained to be good at and then become something necessary.
And now, that skill has become an asset.
Based on the description, referring to the backfire as 'phantom pain', he assumed that the pain would be nothing more than an induced illusion. It was not real but felt like it. In that case, the limitation was not as bad to him.
Just an inconvenience.
Of course, that doesn't mean he could disregard it entirely.
During a vicious battle, that momentary pain might cause an involuntary twitch or pause.
A moment that might cause the end of him so he needed to be careful.
Moreover, Rex now realized the reason why he was sleepy and tired earlier.
He used the Inevitable Death two times during the day, which means he sacrificed a lot of his blood.
