What would prevent Anthropic or Open AI take one of the open source models, tune it to "feel" like one of their models and expose them under their respective na

What would prevent Anthropic or Open AI take one of the open source models, tune it to "feel" like one of their models and expose them under their respective names (GPT or Claude) to save on training and inference, but keep their brand name's popularity? If the models are not objectively worse and are cheaper to run, then nobody would complain, or complaining baseline would stay the same.