“You may also want to get a reentry permit if you plan on traveling outside the United States and cannot or do not wish to get a passport from your home country. Many countries throughout the world may allow you to use a reentry permit much like you would use a passport—placing necessary visas and entry and exit stamps in the permit—so you may use it as your main travel document. Be sure to check with any country you plan to visit about specific requirements before you travel.”
Not sure how many countries would take longer to issue a passport than an REP, though (I know my home country does, but it’s stupidly long). Bear in mind that with ASCs still closed for the next couple of weeks, it will probably take you a while just to get the biometrics for an REP done. Earlier this year (Pre Covid) REPs were taking 3-5 months to be issued, and its almost certainly longer now. Bear in mind if your home country passport usually requires a visa for a particular country you may need one for the REP too, so be sure to check that as well.
Asylees with green cards use RPs and RTDs all the time in lieu of passports since they cannot get one or do not want to use it. It takes 3-4 months to get a RP and needs visas for most countries. Also some countries do not allow entry on RP. Check the Asylum forum which has a thread for travel experiences on RP