Having the icons closer together would also make it more prone to misclicks.
For something as basic as the main home screen, you need proper space to ensure you reliably click on the right icon I think.
Overall, I think the spacing is fine, its really the limitation of 3 screens that is the issue, but there are apps for that, as well as using the native folder option.
But overall its not that bad, just take a little time to organize and keep everything to a minimum. Something like phone settings should be taken off the main screens. Initially you may use it a lot, but after that you are less likely to need it. If you frequently change a specific setting, use a widget for that.