As many of her predecessors have found out, it's one thing to win the leadership vote and a whole other to stay in office. Takaichi's own LDP party is divided into many factions and all want to push their respective agendas at the end of the day. She's pretty much in the hot seat now and one key reason that helped her rise is her alignment being more towards the right wing.
In part, the LDP is also banking on her appeal in that sense to win back some of the conservative base - which have switched to the more right-wing Sanseito party after the recent upper house election results in July. Of course, the Nippon Ishin base is one that also aligns with the right wing but they still have key differences in viewpoints on some matters with the LDP as a whole.
