TL;DR I save money by homebrewing and I, once in a while, spend a little of the savings on beer. But not very often.
If one can’t save money by homebrewing then one, or both, of two things are the problem. Either (1. Building a brewery is a more important part of the hobby than actually making beer is, or, (2. They aren’t brewing enough.
I’ve been brewing for 11 years and for 5 of those years have been brewing 6-8 times a year in a second location with a second (admittedly very ghetto quality) system. At our farm I have a basic, 3-vessel setup with a 10 gallon Igoo MLT, an 8 gallon HLT and a 10 gallon BK. My heat source is a repurposed 2 burner propane camp stove we received as an Xmas gift about 20 years ago. Using that saved a significant part of the startup cost. I also have a dedicated ferm fridge (total cost: free-ninety-nine for the fridge, $35 for an Inkbird) and a 3 tap kegerator (free ninety-nine for the fridge, about $400 for the necessary draft hardware) and 8 kegs (average cost $30 each). Rounding up I’m all in for, maybe, $1200-1300.
At the city house I brew on a BIAB setup, the cost of which would be a rounding error in the cost of many of the systems which members here have put together. I use an 8 gallon turkey fryer which cost, net, $20 (it was on sale for $45 and I had a $25 rewards card from the sporting goods store), 3 five gallon buckets, an IC and the usual assortment of small tools and equipment. I might have $200 in the whole thing.
So, rounding up, I might have $1500-1600 in two breweries. In 11 years I’ve brewed the equivalent of approximately 375 cases of 12 oz bottles. The styles I brew cost, in this part of the world, $8-10 a 6 pack. Average that out to $35 a case and I’ve brewed about $13K worth of beer with less than $2K worth of equipment. Add the cost of ingredients, at an (inflated) average of $25 per batch for 170 batches, and I’ve saved $7K (the ingredient cost is inflated because I’m being conservative and applying the same cost to the smaller batches that I average for 5 gal batches).
So, yeah, it’s possible to save quite a bit by homebrewing. But it has to be about the beer rather than the gear to do so.