Timothy's backlash is more complicated than he realizes right now. As he progresses with managing it, he's going to realize that 'fatigue' and 'exhaustion' are partly psychological constructs. As any college student with a paper due in the morning will intuitively understand, you can be exhausted while being extremely productive. Or you can be passed out after a party. Both of these count as being 'exhausted', but feel quite a bit different.
Tim's plan for using the 'healing silo' to pay off his short-term Esper Loan was to get fifteen to twenty people in a room, and extend his power to cover them. His ability does increase healing, and from what everyone's been able to tell, will let people recover from injuries approximately perfectly. No scar tissue left.
Bad shoulder? Just spend a week in the same room as Tim! Organ damage? Why not? Brain damage? Well, to be frank nobody's volunteered yet, as it seems incredibly fraught. Recovering from surgery? Much better than waiting four to six weeks!