I think the animé really dropped the ball on Goh's goal. I know a lot of people don't like it and with how it's handled, I don't blame them, and I'm one of them, but there actually is a way it could have been made better and even been a good goal, maybe even the best so far. It could have been part of a much larger goal, especially since Mew is said to contain the DNA of all Pokémon. Maybe have Professor Cerise be curious as to how this is the case, especially when there are significantly stronger Pokémon, such as the "box legends", Arceus, and Mewtwo. We could have Cerise hypothesize that Pokémon may, in fact, be a manmade creation with Mew being the origin of all Pokémon. You could have Goh also be interested in this and maybe even have the same hypothesis and have this be the reason why he's on his quest. He wants to help determine if Pokémon are, indeed, a manmade creation.
Of course, to test the hypothesis, Cerise will need as many Pokémon as possible from different species, and would probably prefer to have numerous members of the same species. Hence where Goh comes in and his goal for getting every Pokémon and Mew. Maybe not save Mew for last but have him consider getting Mew last since he would need a lot of strong Pokémon in order to capture the elusive cat-like Pokémon. As for Professor Cerise, once he gets the Pokémon could scan their DNA and do tests on the DNA to see just how similar to Mew they are and, if they are, indeed, engineered, what animals or other things they originally came from. The possibilities would be endless and would give real purpose to Goh's goal. It could open a whole new direction for the story, as well as introduce villains who do not want that question answered at all.
Said villains could even have members of the Pokémon League be a part of them and maybe to make the matter more gray, have it be that their fear is that if Pokémon are, indeed, discovered to be manmade creations, then organizations like Team Rocket will get more power and influence since more trainers may view Pokémon as inferior and not deserving of the rights that they currently have. I could also see Pokémon Poachers taking advantage of the situation as well. Others might not like the implications as well since if one group of scientists managed to create Pokémon, likely from the DNA of Mew, what's to stop another group from doing so?
There are many directions where even just decent writers could go with this, and it would still allow the series to advertise and display a large number of Pokémon. If anything, advertising a large number of Pokémon would be a requirement for such a goal so it would fulfill a requirement for the animé as well and have doing so be natural.