It's not about just picking the next word here, that doesn't at all refuse whether Transformers can achieve AGI. Words are just one representation of information. And whether it resembles any intelligence we know is also not an argument because there is no reason to believe that all intelligence is based on anything we've seen (e.g us, or other animals).
The underlying architecture of Attention & MLPs can surely still depict something which we could call an AGI, and in certain tasks it surely can be considered an AGI already. I also don't know for certain whether we will hit any roadblocks or architectural asymptotes but I haven't come across any well-founded argument that Transformers definitely could not reach AGI.