The amount of string you use to edge is practically free if you buy a big roll. This is all assuming you know what you are doing, and I think that’s the issue here. I mowed yards for 6 years as a kid/teen and mowed my own for years. Sure if you don’t edge it every now it’s going to use more string but I cut weekly and the edges got touched up each time. I could edge as fast as I could walk.
The guys that let the grass grow for weeks or only edge it twice a season? Yeah, the edger makes sense.
I like power equipment but buying another piece for something I can do with a string trimmer doesn’t make sense to me. I pay a lawn service now and still have a 52” walk behind, 3 riders, a Honda HRX, a trimmer, a backpack blower, a handheld blower, a battery powered smaller blower, a backpack mosquito fogger, a pole saw and a chain saw.
OP needs to slow down the string speed and have a bit more finesse and I bet that fixes the problem.