That's not how these drugs work. Think of it in terms of there being a programmable neural network in the gut (and associated brain I/O areas). This network is designed to get the animal to eat appropriately. But food makers figured out ways (by thousands of years of machine learning) to tweak its weights such that it tells the animal to eat too much. GLP-1 works by un-tweaking those weights (not quite: more like it clamps some of the inputs to the network but the result is the same). So it does indeed work by stopping the consumer from eating as much.
That's not how these drugs work. Think of it in terms of there being a programmable neural network in the gut (and associated brain I/O areas). This network is designed to get the animal to eat appropriately. But food makers figured out ways (by thousands of years of machine learning) to tweak its weights such that it tells the animal to eat too much. GLP-1 works by un-tweaking those weights (not quite: more like it clamps some of the inputs to the network but the result is the same). So it does indeed work by stopping the consumer from eating as much.