Specs mater as a quick reference… like you mentioned sensitivity and impedance. But that is it. Let’s say I was buying a new set of speakers I would spend 40 - 100 reading professional reviews, a few hours on forum reviews… of that time, I would have spent maybe five minutes liking at specifications. Then at least 10 hours auditioning speakers. From the specifications you want to make sure you do not make some big mismatch, like really inefficient speakers with a flea powered amp.
Other than this, it is really important not to look at specifications. They will lead you astray nearly every time. The basic foundation of high end audio / Audiophilia is observation (like science). Every component and their interaction is about this. You must listen to them… each person has different values and the true musical performance (sound quality) is not capured by a few variables. This is where many people go wrong and go down dead ends or just get frustrated… you must listen to stuff and master the language describing sound… not make judgements based on a grossly simplified view based on a few basic parameters.