GLP-1s definitely cross the blood-brain barrier - work by affecting the GABAergic CNS and making you not hungry so you stop eating and lose weight. They don't independently do anything to make you slimmer. Basically what you're suggesting is people lose weight, which, I agree.
There is also research showing improvement in Alzheimer's disease symptoms. [2]
[1] https://pubmed.ncbi.nlm.nih.gov/11931352/
[2] https://www.sciencedirect.com/science/article/pii/S221287782...