Illustrator allows to snap stuff to grid, but really doesn’t love doing it (here’s a request about the tolerance and how it’s to harsh in general: http://illustrator.uservoice.com/forums/333657/suggestions/49616738)

Here in a GIF I’m creating a simple path with anchors placed on a grid. After closing the shape, I decide to add several points in-between, and have them on the grid as well... but the only anchor I can place normally is the one in the middle, that happen to be exactly (within an unknow tolerance) at the intersection of the grid lines (and the cursor gets a + to indicate adding would happen).

But for some reason when I try to add an anchor within the magenta circle... a new path gets started.
Well, OK, the path is too far from the grid node, I guess...
But then I try to add a point below the one I was able to place — and it gets added! ...even though it’s not on a grid node at all, but at a grid line... OK, but this happens only if I am zoomed out enough, because if I zoom in — it won’t happen, the tolerance hit is detected in the screen space. And even if I try to add an anchor on a path at a grid line intentionally — Ai won’t let me.

So what we have to do, is to disable Snap to Grid, place points, enable the snapping back, and move each point to snap to grid line intersection again.

This differs from how snapping to grid happens in other editors. If I try the same in Affinity Designer (using Node tool) — it will offer me to place new anchor on intersections with grid lines, like the second GIF shows.
I am also told Fontlab catches a mouse click to see if it hits a path first, then adds the anchor, and only then snaps it to the grid — and it makes practical sense as well.

Perhaps start loving grids?