Agree. It could be an antitrust violation by both enterprises. Even Pulte himself might not be shielded by sovereign immunity if he acted as a market participant rather than as a regulator. There's no chance the current A.G. would bring charges, but if Dems reclaim the A.G. office in 2029 they could bring charges (assuming they can plausibly be made) within the 4-year statute of limitations.
There isn't a Chinese wall between the 2 but they are supposed to be competitive so that there isn't an appearance of a government backed monopoly in the mortgage market. Combining the 2 for a MAGA theoretically should NOT even be on the table.