look at how Trump took power. he is completely hostile to the GOP establishment but he did not start his own party. the Tea Party was a movement but not a 3rd party. they used the GOP as a trojan horse. they blew a path through and took the reins. they understood the system, they used it in their favor, and they remade the institution, bringing generational energy and a national political realignment with them.
if they tried to do that via 3rd party they would be handing elections to the Dems