Do lower control arm reinforcement plates actually work?

The reinforcing plates absolutely make a difference. Boxing the open end of the LCA adds quite a bit of stiffness, and the plates don't really add that much weight. The other thing is that the plates are very useful in keeping the ends of the LCA from spreading apart, which they can do over time. You can see that in @Jim Lusk 's youtube video on adding the plates



I go a step further when I do mine and add a strap right across the back of the LCA where the pivot is. Less flex=more predictable handling

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You do have to pay attention to the location of the strap to make sure it doesn't interfere anywhere
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That same strap application could have been used in place of the fancy aftermarket plates too. I imagine those plates capturing gravel and such.