It seems to me that if your stroke width is odd (e.g. 1), wouldn't it make more sense to have an odd number of pixels so you could perfectly center lines and be aligned to pixels?
However, I've never seen anybody ever recommend using an odd-numbered grid.
Here's an example. If I know I want this icon to always be this size (when that's within my control) and I need it to align to the pixel grid, why is 17x17 not better than 18x18? 
This is only true if you think that the stroke is the basic primitive. If you mainly work with filled shapes then you want to end up on the even gridpoints.
Let us give names to these two ways of working. If you think that the line is the base primitive then your primarily designing items that are stroked. Lets call this stroke priority. If you think that eventually everything is a outlined thing then your designing with outline (shape) priority. and if you belive that the stroke is just accidental and the center spine of the stroke is the true data then your designing with line priority (Engineering applications typically work this way).
Theres nothing wrong with these worldviews. It is not the whole truth. In this case it is typical for people in the graphic design industry to follow outline priority as ther base mode of operation. So it is natural that the tool is geared for this work (in fact for a long time illustrator denied other way of looking at things in its toolset).
When you draw the outlines you want to hit the grid. And the canonical solution for shape priority thinkers is to use a stroke that is on the side of your line (So illustrator has an option for line inside or outside but that only works for closed lines. sigh Just No).
When you draw with stroke priority your situation is as you describe when you have a odd sized stroke. Except if you have a stroke type that just ends at the vertex. In which case you need to hit both center and grid. Offcourse for a even stroke you want to hit the grid.
And again line priority people dont care if they do the want to be on the grid.
Second thing is if you design largest icon first its easier to divide even numbers. But seems to me that for same reason people have different drawing priorities they can also thinkbit the other way around. If you start with smallest icon you dont end with this problem. But it is impossible to center your design at smallest scale.
So depends what you do and how you think about the world.
Usually, 8 point grid is used in the design. This approach allows you to keep the consistency of layouts, and accessibility and allows you to create a hierarchy in layouts.
There is also a 4-point grid, which is a modification of even grids.
Besides, you can also use an odd grid. For example, there are 5 and 7-point grids. Which option selected depends on your needs and ideas.
