Well, it makes things easier for (many) tourists. Trying to hold the characters for a novel script in my head is tremendously more difficult than holding the letters for a new language that use Latin characters.

You can still transliterate into English without overhauling your entire orthography.

Portuguese uses Latin letters, but good luck pronouncing even half the words correctly without a lot of practice.

True, though foreigners who can read the Latin script can at least recognize names on Portuguese signs, which helps with getting around (as long as you don't have to speak the name out loud). That's half the reason Greece provides Latin names on signs everywhere. With a sign that says "Χανιά | Chania", your average foreigner isn't going to pronounce it correctly either way (the "ch" is supposed to be like "loch", not like "chess"), but at least with a Latin version appended they're more likely to find where they're going.