The precogs serve a purpose within the deck, they are used to show how many creature control spells your opponent can level against you before you commit to floating eternity. In some cases they are useful for other purposes as well, revealing quakes, explosions, parallel universes and miracles so you can adjust your strategy. They do also do not slow the deck down as a normal card would, due to their cantrip nature.
For this deck, damage should not be a big issue if you are adaptive with your strategy (easier said than done, despite how straightforward and inflexible the deck appears ‘on paper’), whether it is with rewinding your own field for a rush pass miracle or being creative with your use of parallel universe. Elidnis especially, if you have phase shields backed up, let Elidnis grow her forest spirits and copy them when they are large, the combination of immaterial creatures + feral bond is the only significant heal that cannot be bypassed with this deck, but in most circumstances, it doesn’t heal Elidnis for enough to matter.
Personally, I think 4 SoGs are adequate, though adding more would certainly help against a few of the gods, Octane especially (against whom keeping them alive becomes a central strategy). The reasoning for 4 is that it’s the amount that I’ve found is able to just cope with accumulated poison prior to establishing deck control and momentumed creatures getting past the shield