The real problem is that big companies are structured into hierarchies, and getting a big change (like a site redesign) often requires simultaneously developing support through several branches of the company tree. At each level, management feels an obligation to make their opinions felt, and the result is endless compromise. For some things, this works well, but it is a very risk-averse process, so it is hard to make dramatic improvements. So big companies buy little companies (and often ruin them, but that's another discussion).

The problem isn't necessarily that big companies have incapable web designers, but rather that the influence of even the most capable is quite limited. It seems to be a fundamental problem with large organizations.