I think "run it out" phases likely signal to the lifter and coach that the programming is no longer productive and it needs to be modified.
There are two assumptions in here that I would like to clarify.I realized I forgot to mention my progress in my OP, so sorry about that. I've been doing the program for over two months now, and I imagine eating for recovery might be important now more than ever as I'm getting closer to handling true 1RM's.
1) Eating for recovery in the context of a normal weight individual who is not actively hemorrhaging weight is not a thing. If you eat more, you can placebo yourself into lifting more weight. If you gain body weight, you likely will have a bit more LBM than someone not gaining weight and this can directly help with performance to some extent (though not day to day).
2) You're probably not handling weights closer to your 1RM's, as your 1RM is constantly changing. A 5rm is 85% or so of your 1RM and has a certain amount of fatigue, likely more than a triple at 86% (which is not a 3RM). I do not think eating for recovery significantly changes this. Additionally, I would not recommend the 5> 3> 1 progression on TM unless peaking for a meet.