I think it is important for people to test everything. I tested both gas torch and induction annealing and saw no changes on the target. Gave each method a solid 100 rnd shake down on 6x fired brass to see if it made a difference. I just recently tried the induction annealing again with my 20 Vartarg and my 22BR with no measurable improvement at 300 yards.I'm not going to argue BEP but I can tell you as I'm sure many others can that annealing after each firing keeps the load pressure and consistency better and after all it's that 1 small hole or all 11s what we are after?
I am in a unique situation of having an industrial induction heater available at work to play with, but anyone can try out gas torch annealing without laying out hundreds of dollars for a commercial system to see if it reaps rewards for them. If you use a lot of neck tension or have to generously size your brass for functionality in a hunting or PRS gun, then you may see more benefit than a guy like me that single feeds his BR rifles rounds that have basically zero shoulder bump (just enough to maintain a smooth bolt close) and 0.001" of neck tension.
There's also placebo. If you like doing it and it makes you feel more confident in your process, then that isn't without value. The AMP is just very expensive if you aren't sure that it will give you that reward. That said, if you know you want an annealer, the AMP is the best setup available.
Just my 0.02