The problem is that when you are using the standard roman alphabet, whether as a transliteration or transcription, the graphemes may have different values for different languages and according to the orthography used to write the language used by the person making the transliteration or transcription. Further, you may be comparing a transliteration or transcription with an etymological orthography.
As an example, <ll> has different values in the orthographies used to write English, Welsh, Spanish and Italian. Not only that but the sound represented by <ll> in writing Spanish is represented by <lh> in Portuguese and by <gl> in Italian. That means that looking at what is on the page you can see similarities which in fact only exist in writing and may miss cognates because they are not apparent from writing. And that is when looking at languages which have been written in roman script for centuries. When you start comparing such languages (and remember some have orthographies more etymological than others) with transliterations or transcriptions of languages traditionally written in other scripts the possibility of being misled multiplies.
Equally, orthography may be a reliable guide. Despite the fact that <g> before <i> represents different sounds in English, French, Spanish and Italian we know that <religion> (English and French) <religión> (Spanish) and <religione> (Italian) are "all the same word" - the <g> has in all cases been carried forward from Latin <religio> (with in fact yet another values for <g>).
I was hasty. Transliteration as a technique can be of course how you can compare different languages, I was mostly reacting to basically everything you wrote in this post.