Thinking back on it a little more, a corollary game for how last night played out that didn't work out was the Eric Haase defensive meltdown game in Minneapolis. Soto wasn't on a leash that night, and to the extent anybody may have gotten up to start warming in the BP (I believe it was Barnes IIRC), it seemed less about relieving Soto in that moment and more about preparing for extra innings.
The situation isn't entirely the same (other leverage relievers had been used, Will Vest was viewed differently at the time, Chafin was still on IL, etc.), but having said that, Hinch does deserve some credit for acting as quickly as he did last night and it may be a sign that Soto is on a shorter leash now.