There is actually an IC for that too:
https://ww1.microchip.com/downloads/en/DeviceDoc/mic5159.pdfMIC5156 to 5158 also (wide voltage range), the latter two (7 and 8 ) which have a charge pump to power an N-ch output!
Most of them don't have current limiting (indeed most of the examples in the linked datasheet, don't show current limiting; how do they show a ~constant-power limit curve then..?!).
Family e.g. here:
https://www.digikey.com/products/en/integrated-circuits-ics/pmic-voltage-regulators-linear-regulator-controllers/757A lot are the more specialized type, an N-ch source follower. Compensation is much easier, but to get low dropout, the controller needs a higher supply voltage. It's convenient, when you can get away with it. A good use-case is a system with 12V available, needing a handful of outputs say 1.8-3.3V, supplied from 5V.
Or the lower voltage version, which you might use to get 1.8, 2.5V etc. from a 3.3V common rail, when 5V is handy. Here's an integrated one:
https://www.ti.com/lit/ds/symlink/tps74801.pdfTim