A narcissist like Trump who sees everyone and everything an extension of himself will not be happy about nominating a "heir"...someone who is expected to not only continue his legacy but improve upon it.
And the Republican party will only back Trump's son if they have reason to believe he can do that.
The Republicans picked W. because he brought them TX after taking out its Dem governor Ann Richards. They didn't do it because they admired HW and wanted to rally to him. Don Jr. will only be a viable candidate if he can prove himself capable of winning. There was talk about Don Jr. running for Mayor of NYC against the unpopular Bill de Blasio but given (as yesterday proved) how much the city thoroughly despises the family unconditionally, it's unlikely. And Trump publicly told a major network that Don Jr. has no chance (https://www.nbcnewyork.com/news/poli...mayor/2658590/). I mean aside from everything else, Trump is a s--ty parent. So if Don Jr. or Ivanka are ever to be forces in US Politics, realistically speaking it's not going to be in 2024 just as W. wasn't a realistic possibility in 1996 remember.
Likewise Trump in 2016 had the aura of a "billionaire", a successful TV show ("The Apprentice"). In 2024, everyone will know this family isn't remotely as rich as it pretends, it has debts coming in, lawsuits in the offing. Remember the majority of Republicans didn't vote for Trump in the primaries, he came through via Winner Take All and Vote-Splitting. The other thing is that Donald Trump has a certain quality that puts him above Don Jr. and Ivanka...he happens to be funny, in a crude insult-comic standup sort of way. He's a showman and entertainer and carnival man, and the Trumpspawn don't have those elements. So they won't have the advantages in 2024 that Trump did in 2016.
For the GOP, Marco Rubio is shaping up to be a prospective candidate, hoping to maximize their hitherto unknown Latino voter base. Rubio is a bit of a clown himself (and is rumored to be gay) but he might allow the GOP base for a "fresh start" and put the Dems in an awkward position of wanting to field against the prospective first Hispanic President, and the rumors of closet homosexuality will be hard for them to work with without coming of as hypocrites and jerks. Barney Frank might try and out Rubio if he says homophobic things which might work. Rubio seems to be well liked and more likable than for instance Ted Cruz. So he might work as a sort of Hispanic Romney.