Why does uniquelist=false option of biblatex package work only if it is inserted at the first time?

The option uniquelist=false, should work as advertised no matter when you add it to your document, but since the option affects calculations done by Biber (the backend) it may not show an immediate effect when you only run LaTeX after you added the option. When you change options that affect Biber, you should rerun the full LaTeX, Biber, LaTeX, LaTeX compilation cycle to be sure that the new settings are used.

Unlike in some other cases, biblatex does not automatically warn you that you have to rerun Biber in order to be sure the option change has taken effect. In theory it would be possible to implement a check for this in biblatex and Biber, but it would not be completely trivial either and so far no one has asked for it. If you think that an automatic warning would be useful you can always open a feature request at https://github.com/plk/biblatex/issues.

From your description it sounds as if you only ran LaTeX after you added the option. When you deleted the .bbl file you (or your editor) had to rerun Biber and at that point the option finally took effect.

I'm guessing that you are using an editor or some other tool that normally runs Biber for you automatically. Presumably that tool did not manage to detect that a Biber rerun was necessary. That's not too surprising since biblatex does not warn you about this. However, some tools have extremely advanced heuristics and can already detect situations like this and rerun Biber for you (the wonderful latexmk comes to mind). If you are not using such an advanced tool, the only thing you can do at the moment is to make sure to rerun LaTeX, Biber, LaTeX, LaTeX manually. (You certainly don't have to delete the .bbl file for that, your editor should offer you an option to do that manually, but if that is the easiest way to get the full rerun, why not?)