Non-citizens at US points of entry have very limited constitutional protection. SCOTUS has consistently held that the federal government has broad authority over immigration and border control. Basically nobody has a 1st or 2nd amendment protection at a border crossing, and non-citizens have further-restricted 4th and 5th amendment protections among others.
Border agents do not need any level of suspicion or probably cause to search your person or your effects. Failing to answer questions can result in entry being denied. US v. Ramsey held that everyone, citizen or not, has no inherent right to enter the US at a particular point of entry on a particular date and time and that basically any search is "reasonable" due to national security and law enforcement needs. That ruling was half a century ago.
Shaughnessy v. US ex rel. Mezei (1953) held that even a lawful resident who is re-entering the country after an absence can be denied re-entry without a hearing as long as that denial is lawful. Mezei lived in the US as a lawful immigrant from 1923 to 1948 then went back to Hungary for just over a year and a half. A 1924 law classified him as an "excludable alien" when he returned in 1950 he was permanently barred from re-entry. This was before LPR status was codified so I imagine there is more relevant case law to that classification specifically.
SCOTUS has consistently held multiple distinctions between citizens and non-citizens at the border: Citizens have an absolute right to enter the country, non-citizens (including LPRs) do not. Everyone loses most 4A protections at points of entry, but citizens have a reasonableness bar that non-citizens do not (US v. Montoya de Hernandez 1985, US v. Flores-Montano 2004). Citizens still enjoy due process while non-citizens do not (Shaughnessy again, Kwong Hai Chew v. Colding 1953). Citizenship ensures someone is not in a legal limbo status of being detained unreasonably or indefinitely (Boumediene v. Bush 2008), a non-citizen denied entry without the means to leave is basically stuck there. Citizens are presumed able to enter the country and have faster processing, all non-citizens including LPRs must prove admissibility every time.
So there's a century (or more) of case law supporting what some might call extreme power on the part of the federal government to deny non-citizens entry at any port of entry, for any or no reason. But what it boils down to is whether there are any countries in the world that don't have this policy? There is no country in the world where as a non-citizen I enjoy the same rights and legal recourse as a citizen if I am denied entry, and no country where it is not on me to affirmatively prove to the border agent(s) that I am legally permitted entry. It is always a privilege to enter a country other than your own.
Edit: At the risk of breaking guidelines and making for boring reading, I have to question the odds of someone being able to read this comment in ~30 seconds, process the argument, and decide its worth a downvote vs. "oh I don't like this first sentence."
