I know for a fact that OTPs were used by diplomatic corps of a certain unnamed country as recently as under 5 years ago.
As for specific info on OTP use by US diplomatic corps, see the interesting Wikileaks cable below requesting Teletype based OTP comms support for the Pope during his visit to communist Poland during the Solidarity crackdown.
(U) URGENT COMMUNICATIONS SUPPORT NEEDS AT KRAKOW DURING PAPAL VISIT
Date:1979 May 11, 00:00 (Friday)
Original Classification:CONFIDENTIAL Current Classification:UNCLASSIFIED
034505; (D) WARSAW 0942
- (C) SUMMARY: WE HAVE REEVALUATED OUR NEED FOR SECURE COMMUNICATIONS SUPPORT AT KRAKOW DURING THE PAPAL VISIT. OUR CONCLUSION IS THAT REF. A UNDERESTIMATES THE POSSIBLE NEED FOR FAST,
SECURE COMMUNICATIONS DURING AN EVENT OF THIS MAGNITUDE IN
POLAND AND OVERESTIMATES THE COST OF THE SORT OF "CAN-DO"
PACKAGE OPERATION WE BELIEVE WOULD REPRESENT A WISE PRECAUTION
IN THIS CASE. WE WILL REQUIRE TDY COMMUNICATIONS SUPPORT IN
ANY EVENT; WE RECOMMEND SPENDING A LITTLE MORE TO BE PREPARED
FOR ANY EVENTUALITY IN WHAT COULD BE A VERY VOLATILE POLITICAL
SITUATION. END SUMMARY.
- (C) KRAKOW COMMUNICATIONS FACILITIES: CURRENT SECURE COMMUNICATIONS FACILITIES, AS DESCRIBED IN REF D, CONSIST OF A TELEX AND A
ONE-TIME PAD, OPERATED BY WHICHEVER OFFICER (P.O., VICE CONSUL,
OR BPAO) CAN BE SPARED FROM HIS PRIMARY DUTIES. IN AN EMERGENCY
THE FASTEST WAY TO GET A MEDIUM-LENGTH, URGENT, CLASSIFIED
MESSAGE FROM THE CONSULATE TO THE EMBASSY RIGHT NOW IS TO JUMP
INTO A CAR AND DRIVE FOR FOUR TO FIVE HOURS. DURING THE PAPAL
VISIT EVEN THIS MAY NOT BE POSSIBLE SINCE, WE UNDERSTAND,
STRINGENT TRAFFIC CONTROLS WILL BE EXERCISED IN AND AROUND ALL
LOCALITIES TO BE VISITED BY POPE. HE WILL BE IN THE KRAKOW
AREA FOR FOUR DAYS (JUNE 7-10).
Another cable from the same era alludes to use of OTP for emergency comms during a tropical storm but also says OTP the only means of secure comms since electronic comms are not functioning:
- AS RESULT OF CYCLONE, EMBASSY HAS BEEN UNABLE TO SEND OR RECEIVE
TELEGRAMS SINCE NIGHT OF 22ND. NEW EMBASSY STANDBY GENERATOR STILL
NOT CONNECTED DUE VARIOUS LOCAL INEFFICIENCY. PREVIOUSLY SCHEDULED
COMMTECH TEAM ARRIVING JAN 2 FOR RADIO INSTALLATIONS. THEY PRESUMABLY
WILL BE OF ASSISTANCE IN FINISHING GENERATOR INSTALLATION.
SHOULD FURTHER PROBLEMS DEVELOPE ON RECENTLY RECOMMENCED CITY
POWER, IT MAY BE NECESSARY TO USE ONE-TIME-PAD FOR ANY URGENT
I take that to mean that paper based OTPs may need to be used.
It is possible and even probable that the use of OTP continued long after 1979 by the US government.