Yes, you are perfectly right: You need to look at both gradients (eg. horizontal and vertical).
However, depending on the orientation of the polygon, one gradient will have a significantly bigger step-size than the other one.
(That's for steep angles when both gradients are not approx. orthonormal)
So which mipmap do you take? The larger, the smaller, one in the middle?
You can only match both gradients with anisotropic mipmaps (aka ripmaps).
That's fine if you can pick a single ripmap for the whole triangle but awful lot of extra trouble when constantly recalculating linear deltas in a perspective corrected texture mapper.
One approach to handle this properly would be to split your triangle in the screen-space into eg. 8x8 blocks and interpolate uv bilinearly (instead of subdividing each scanline separately as you woul'd with the usual perspective correction approach).
edit: Oh, I just realized I already suggested that 3 years ago