Hrrrg Tim didn't become Robin (after trying to convince Dick to be Robin again) because he was worried Batman would go too far or was beating criminals too hard (he was, Tim didn't gaf about that)
Tim did all that because he was worried about Bruce.
"He was hurt but that didn't stop him. Nothing stops him". At this point Bruce is getting injured and just going on and on. (This is also the only time Tim was following Bruce around with a camera) Alfred agrees with that assessment
These are all from Batman (1940) #440, the first issue in A Lonely Place of Dying. In #441 Tim tells Dick:
Tim is explicitly worried about Bruce, not the people Bruce is violent towards.