Someone who speaks a language written in a latin script can approximately pronounce Hungarian words by sight, even if they mispronounce digraphs and ignore diacritics. Familiarity with the script alone will aid one-way verbal communication between a tourist and a Hungarian-speaker. A tourist who can sound out "Keleti" or "Nyugati" (instead of the hypothetical cyrillic "Kэлэти" and "Нюгати") will be guided to the respective railway station, and even a relatively intimidating word like "Határátkelő", when mispronounced Ha-tar-at-ke-lo" will be understood as a border crossing. This is the same reason the Moscow Metro includes latin-transcribed station names on the official map [1].

Going the other direction, Hungarians can learn many European languages easier than Russian, because the script is the same, which makes orthography and pronunciation easier to reason about, and vocabulary easier to acquire.

[1] https://www.artlebedev.com/metro/map3/

When glyphs are recognizable, it is still better. If not for informational messages, at least names of the locations can be somewhat recalled. Let's say I drive and I need to go to Székesfehérvár. I have only a slightest idea how to pronounce it, but I will recognize it. Much harder to do if you need to drive to กรุงเทพมหานคร

Hungarian (and Finnish) are unique cases; you haven’t identified a pattern, but the Uralic exceptions. It’s a language family only 25 million people on Earth speak, it is the proverbial exception proving the rule.

emodendroket - in the case of Quebec, they've moved heavily towards French only (currently, French predominantly). I have zero issue with this and it would beat everything looking like my emails from corporate where they're blocks of FR/EN/ES or EN/FR/ES translated scripts. Works fine in emails, not sure how I'd feel looking at things out and about having a ton of translations though.

If you really want the signs to be intelligible to foreign visitors you can likely more easily do what many other countries do and provide signage in English. This seems like a weak rationale to change how the language is written.