The problem with this sort of econ-101 analysis is that, sure, "it stands to reason" in a simple economic model. But the question is if it stands to reality where there's a lot more going on.
And even if it is true in a world of sticky wages, regulation and a hundred other things, economists tend to stop their analysis there[1]. What are the second-order effects of the poor having more money? Almost all of that will be spent, so there's a multiplier effect, and I'd expect, e.g., MacDonald's extra dollar in salary to actually cost less, because some of that money will come back. (This isn't different in principle than SNAP, for instance, which generates much more than a dollar of economic activity for each dollar spent.)
Veering in a slightly different direction, if some companies would stop fighting minimum-wage increases so hard, I might have more sympathy for their endless moaning about corporate tax rates. If they didn't use the safety net to subsidize their low wages, perhaps we could unwind some of these absurdly convoluted payment structures[2].
And finally, I'm simply done with arguments like this. There is so much inefficiency, bullshit work (that term used in the technical sense), barely disguised corporate graft on top of a historic shifting of the tax burden away from the wealthy combined with actual market forces that are concentrating wealth that I feel like even if a modest minimum wage bump were to create a noticeable shift in statistical measures[3], it would still be too little done to help those struggling under the weight of the laundry-list above.
[1] "If you want a happy ending, stop the story there." The same holds for sad stories.
[2] Which are the real reason we have waste and graft. If there's one thing investment banks, car payment finance and low-rent advertisements for get-rich-quick scams demonstrate well, if you are in a position make anything involving money complicated enough, you can do quite nicely skimming off the top. Sunlight and simplicity make all that much better.
[3] Notice how little real-world evidence of minimum wage increases causing economic harm there is. Almost all the arguments are instead from first-principles. We've raised it quite a few times, and a lot of people don't like it. And yet, there is almost no evidence it has ever caused harm.