Are there advantages to not killing Big Daddies in BioShock?

Other than maybe saving ammo and so on, there is no advantage to not killing them.

There is an advantage to killing them:

You can rescue or harvest the Little Sisters they guard after killing them, which lets you get more powerups. (Not all BDs guard Little Sisters.)

And you do need to kill at least 3:

Two in Haphaestus in order to complete the EMP bomb, and one when you're escorting a Little Sister.

You have nothing to gain and everything to lose by not killing the Big Daddies guarding the little sisters.

The only source of ADAM in the game (the currency you upgrade your plasmids and self with) is from little sisters. You can only get to the little sisters by going through the Big Daddies. Without tonics, plasmids, and other ADAM bought upgrades, your game will be made exponentially more difficult. This is not the way to play Bioshock on a first playthrough. A minimum Big Daddy run is something for another playthrough challenge.

There are no less than 3 Big Daddies you will be forced to fight before the game allows you to continue, so you will have to fight them at some point.

To receive the best possible outcome in the game, you will need to fight the Big Daddies and retrieve the Little Sisters. What you decide to do with them is up to you...

No, it is not possible to complete the game without killing any Big Daddies, as you will be forced to kill some in order to

collect the necessary parts to finish the EMP bomb in Hephaestus.

Not killing a Big Daddy means you won't be able to harvest or rescue the corresponding Little Sister, so you won't get any ADAM for buying upgrades. The only advantage of avoiding a Big Daddy is that they are challenging enemies to deal with, so you save some ammo and health kits by not having to fight them.

However, there are achievements for dealing with all the Little Sisters in the game, and rescuing all of them will give you a different ending, so you'll probably want to kill all the Big Daddies.