Why does no one put a period after the P in R.I.P.?

Clearly not noone; but there is a global movement in English away from using periods in abbreviations and acronyms—hence RIP rather than R.I.P.

The intermediate form R.I.P looks odd for a reason—why keep some periods in an acronym and not others? But the motivation for it is that abbreviations have been dropping their final period in general: Dr vs Dr., see Why do we have two rules for putting a period after abbreviations?. People who write R.I.P are extending the avoidance of final period in abbreviations, as a hypercorrection, to acronyms.