“The problem is that Trump doesn’t get to select anyone to head the RNC.”
This is wrong. By tradition, when a Republican wins the presidency, they choose the RNC chair. Trump chose Romney. Yes, she then had to be voted in, but she was unopposed, as was the tradition.
So-called "tradition" can be broken at any time. He wasn't President in August of this year when she was re-elected, so he had no any real political power to influence anyone on the Committee. What I said in my original comment, was that he can recommend someone, but he plays no part in the person's election. The RNC Committee members who vote her in, aren't obligated to vote for her, despite even a sitting-President choosing who he supports.
Original comment: "Trump could recommend her, and support her, but he doesn't get to put her in the post, and he doesn't get to vote."