Rerouting problem at start of navigation

You mean change the nearest route point to nearest turn instruction.
Interesting idea. Though cases exist where instructions are very far.

In above example (skipping start) would mean reroute to destination.

Yes, and the resulting route (in above example), would be how a human would expect nearest point on route should look like. But the above example is to short to test, as it does not have any turn instructions at all.
The idea is, when there is a turn instruction there must be some kind of intersection as well.
So my hope would be, that it is less likely that you are routed back and forth on the same road.
I am aware that this is not guaranteed.