I think you've kind of answered the question with Puerto Rico as to why it isn't a State yet; internal political debate on changing its status. Both political parties in the United States have in their official platforms the official endorsement of such and both have repeatedly backed the many votes on the issue of the past decade in an effort to resolve exactly this question.
I do not think that is an accurate representation. When I do a
Google search with the keywords "Republicans" and "statehood" and "Puerto Rico", the top recent hits relate to Republicans being reluctant.
Young, drawing on Alaska’s example, said the partisan tilt of Puerto Rico’s electorate shouldn’t guide the decision.
www.ktoo.org
The above article notes how a Republican representative from Alaska has broken from a Republican consensus critical of Puerto Rican statehood, arguing that there is no reason to assume it must be Democratic-leaning.
Puerto Rico residents are on record as favoring statehood, but partisan concerns might complicate efforts to admit the island territory to the union.
www.rollcall.com
This article notes how Republicans generally, if not uniformly, base their opposition to Puerto Rican statehood on fears that the state will learn Democratic.
About half of all Democrats support statehood for both Washington, D.C. and Puerto Rico, while only one-quarter of Republicans agree, according to a new poll.
www.newsweek.com
This article notes how, in a poll, Democratic respondents consistently were twice as likely as Republicans to favour statehood for Puerto Rico and Washington D.C.
The Republican Party might say it favours Puerto Rican statehood, but in actual fact its membership has demonstrated itself very reluctant. The unspoken but real subtext, of the Republican Party being skeptical about admitting to the Union a populous island full of Hispanics who can be expected to be Democratic-leaning, is real.
Immigration into the United States has never altered political institutions? One I can immediately think of is how immigration into California fundamentally changed its political character, for example, and that's related to this topic.
The self-marginalization of California Republicans because of their perception as a political faction hostile to California's single largest population is ephemeral. California has stayed republican in format, for instance, has remained a polity with competitive democratic elections and referenda, has kept key institutions of governance and law since the state's foundation, and so on. Immigration has not changed that; California's institutions, if anything, have provided a matrix for immigrant integration.
The massive annexations of Mexican territory that you are talking about are wholly different. If Republicans are reluctant to bring into the Union a Puerto Rico already deeply integrated into the US, with millions of American citizens and a high-income economy, how much less likely will Republicans—even Democrats—be to bring into the US much poorer and more populous states with no history of deep integration?