There are insane positions in infinite chess, a kind of chess warfare, involving a bishop gun battery, where black can fire arbitrarily large bishop guns; each bishop moving out is a kind of bullet, and white must answer at every step. But white ultimately wins, even though black, "doomed", has these various harassment possibilities.
The V-E+R follows the pattern of zero-dimensional, one-dimensional, two-dimensional, and this alternating sum formulation continues for the Euler characteristic in higher dimensions. So that is one reason to keep V-E+R.
Another reason, however, is that although some negative numbers show up, the numbers are all very small, and this could be a good opportunity to introduce some exposure to negative numbers.
