# Why density functional theory favors a uniform electron density?

Why density functional theory (DFT) favors a uniform electron density when we use it to calculate ground state electronic structure self-consistently?

For example, when we use DFT for calculating the (ground state) electron density of two $$\text{H}$$ atoms with a separation somewhat larger then the bond length of an $$\text{H}_2$$ molecule, there will still be a non-negligible electron density between the two atoms as if there is still a covalent bond. As a result, the calculated electronic ground state is essentially an excited state of the system.

I cannot remember where did I read this, and I don't understand why DFT has such a problem. I think the problem resides in the fact that we use a local exchange-correlation functional $$E_{XC}$$ like LDA and GGA. But I don't understand why a local $$E_{XC}$$ will lead to a uniform electron density.