It's true the writing system doesn't make it ideal for a global lingua franca, but one of the main advantages I appreciate about it is its ability to disambiguate common strings.

In the Latin+Hindu-Arabic numeral world, we tend to argue about the best way to write dates, everything from 99/9/19 to 2037.04.01 to 4/1 or 13/5/2003 to 5/15/2019. The ISO published a standard, people more or less try to follow it, but in common usage it is still fairly ambiguous.

Without knowing any Chinese or Japanese though, you can probably figure out what this means: 2018年04月05日 or 2018年4月5日

Personally I find this to be beautiful in its simplicity. We tend to use a separator anyway, dots or slashes or dashes or what have you, but add one kanji as a suffix and nobody will argue about whether 4/5/2018 is April 5th or May 4th because 日 (once you've learned what it means) will clearly mark the day and 月 will clearly mark the month.

You could approximate this with Latin characters too, say 2018Y04M05D, but I think there is something to be said for having a distinct ideograph to improve readability and unambiguously mark a day, month, year, hour, minute or second.

I wouldn't say all of written Chinese would make for a good lingua franca, but a limited subset seeing more use globally would be very cool.