..although the C2 takes a slightly different route through Mayfair from that formerly taken by the 8 (and before that the 25) - it enters Mayfair from Regent Street, and doesn't go along any section of Oxford Street at all (as part of Boris's plans to reduce bus congestion along that road).
Actually there have been a number of route extensions in recent years in London, not close to recreating the old lengthy cross-town routes, but a definite step away from the shorter routes of recent years: the extension of the 88 from Oxford Circus up to Camden Town is one (giving a cross town link from Clapham); and that of the 170 (from Roehampton) being extended from Clapham Junction to Victoria being two prominent, and central , examples. Or the 99, formerly Woolwich-Erith, being extended onto Bexleyheath by quite a roundabout route, being one further out.
I suspect that these extensions may, in part, result from the widespread usage of Oyster (and discouragement of cash fares) having significantly reduced dwell time at stops for one-person operated buses in London