It most certainly does not!
I think you could more or less accurately make that claim about Standard Arabic, which has preserved a distinct sound for each letter and only rarely does things that you wouldn’t expect (tanween…).
Modern Hebrew, by contrast, has merged many consonant sounds without merging their letters (sin and samekh, tav and tet), dropped the ayin sound and left the letter as a pseudo-vowel, and decoupled long vowel sounds from their long vowel carrier letters to the point that they’re essentially arbitrary (for each letter, you can find an example of it representing every single vowel sound).
To your main point, though, the main commonality between Semitic scripts and western Latin/Greek-derived scripts is the rough order of the letters and some of the shapes. Latin alphabet isn’t an abjad, it has lots of letters that have no equivalent in Semitic… and it actually represents many languages very faithfully! English is an outlier. So I am not convinced by your argument.