Why it matters when you are writing
The appeal is separation of concerns. Your .bib file holds the facts about each source; the style file decides how those facts are punctuated and ordered. Change the bibliography style and the entire list re-formats, which is what makes BibTeX worth the setup cost when you are submitting the same manuscript to journals with different requirements.
Two things break more BibTeX builds than anything else. The first is capitalization: many styles lowercase titles, so a proper noun needs protecting inside braces — title = {Framing Uncertainty in {P}olicy {T}exts} — or it will come out wrong and you will not notice until the proofs. The second is duplicate or unstable citation keys, which is why a convention like surnameYearFirstword is worth adopting on day one.
Entries exported from publisher sites and databases are convenient and frequently wrong: missing DOIs, journal names abbreviated inconsistently, page ranges with the wrong dash, author fields that mangle particles like “van der.” Treat an export as a draft. Reading the .bib file once, in full, before you submit is faster than answering a copy editor’s queries afterward.