Mike I've never run 1/4" rod, and would like to see it, try it (in person). But that sounds like it may throw a 120v MIG off-topic?
Most people who have 120v MIGs don't share amps with a 9" grinder. (maybe a washing machine though!) They just wanna know ---- for the occasional thicker bracket ---- how to prepare and execute a weld on a thicker piece, if it becomes necessary. Post a question, and get CIVIL WELDING ASSISTANCE on TBN. They don't need to be told to buy a 240v machine then call the electrician to re-wire the garage for 240v -----> for one bracket.
They wanna repair a deck chair or BBQ, weld a muffler, which is near impossible to stick-weld (for an occasional weldOR) but just "easy" to MIG. Which is why they bought into the small "MIG" program. It's a very useful tool.
As mentioned before (cue up broken record

), my entire 5-foot bucket on my Kubota 2710 is made of 3/16 with a few 1/4" brackets, and a 3/8" cutting edge. The entire FEL loader arm assembly has nothing thicker than 1/4", even the brackets for the hydraulic cylinders. Aside from the cutting edge, a 120v MIG (a Miller 135, 140, certainly others) could weld this bucket together very nicely, not be over-driven. And arguably, an experienced welder could get the the 3/8" cutting edge to stick "good enough" = "never break".
I suspect member projects are generally much smaller than constructing an entire FEL assembly for a 30hp tractor. A good 120v MIG can be a very useful tool. Some are better than others, IMHO, of course.
Thanks very much for your even-handed approach. If I sound touchy on this subject its because EVERY 120v MIG thread (if it ever gets the attention of an experienced weldOR) goes off in the direction of "How I'd do it with a bigger machine". Of course anybody who has a bigger machine would use it. Understood how this causes a GAP in the 120v MIG assistance, but
120v MIG owner wants help with the machine that he HAS, can't make much use of assistance of tips for a bigger machine.