Indeed.

I just checked the boarding passes and IDs for a group of people whom I know to frequently have their name order switched from presented ID. Of the last several hundred such boarding passes with name order opposite that of some US-issued ID used for US-departing domestic and international flights, zero rejections by TSA. The most common problems from this: getting frequent flyer program credit for the flight — manual/missing flight credit usually works — and getting elite status recognition from the airlines’ systems. Even Precheck most commonly still showed up on those boarding passes for PreCheck-eligible flights at the time.