Not necessarily.
Every known abjad, abugida and alphabet can be traced back, one way or another, to Proto-Sinaitic Script, either by evolution or inspiration. (Hangul was probably at least inspired by Brahmic scripts, for example.)
Of course, it may well be that an alphabet arrived IOTL at just the right time for it to be adopted, without the need to create a separate one.
It suppose it's possible that a Katakana equivalent develops for Indo-European languages in time, evolved out of Cuneiform (Hittite was written in Cuneiform, after all).
Well that just goes to show that you need to have it be invented one time for it to spread like wildfire, in human chronological terms.
The population of the world around 1500-1000 BCE is smaller, less urbanized, less under politically complex system than it would be later as centuries pass, as iron spreads, as more region come under rule of complex societies, as trade intensifies, as better agricultural techniques develop and the general population grows and more specialization occurs.
If the small region from Sinai to the southern levant managed to develop it from earlier Egyptian hieroglyphics half a millennium into the Bronze Age, it seems natural to me that someone somewhere would develop it either from cuneiform or Egyptian hieroglyphics or that it would develop from parallel writing systems that would have naturally developed elsewhere during the iron age.
A similar thing goes with coinage, it's not like the Western Anatolians had to invent it right there and then for it to eventually appear, given how fast it spread it seems clear that it filled a need that would have pushed people to develop it.
Proto-Sinaitic developed more than three and a half thousand years ago. Surely someone else could have developed an alphabet separately at some point. As far as anyone knows, at least, they didn't.
I mean by about the start of the common era most of the world population lived in societies that used scripts derived from proto-Sinaitic, considering Rome, India and Iran.
Another quarter was already under strong influence by the Chinese parallel development and 1/8 of the world population was in the Americas and Oceania.
Who could have developed a parallel system so quickly just in time to not get the idea from the Near East? Especially as India had to adopt writing altogether.