Eyelets are pretty straightforward and uncomplicated, but they do impact the look of your shoe.
The number of eyelets you choose should depend on the aesthetic you’re aiming for. A Frenchy-type shoe may experiment with one eyelet, maybe two for example.
I like to have at least two to three eyelets because one can look a bit elfish. It’s definitely more stylized.
Plus, fewer eyelets means less lacing and reinforcement. More lacing will better secure your feet (which is why loafers are more difficult to fit and can wiggle loose).
Boots are a bit more complicated. I would advise people to use their best judgement. It’s also dictated by the style and function of the shoe (will it be used for hunting or casual wear?). If you’re in the hands of a competent brand or shoemaker you should be fine.
Fewer eyelets (4 or less) can really complement derbies. It makes the shoe look more casual and quirky.
Some bespoke people choose six eyelets to show off that their bespoke-made shoe. I’d personally avoid this because it errs towards garishness and crowds the shoe.
For the typical office shoe, 5 eyelets is an excellent number. It checks off all the boxes: classic, sleek, and very proportional.