Well the mismatching of streets downtown on either side of Burrard is because, prior to incorporating together in 1886, there were two separate town sites on the downtown peninsula. East of Burrard was "Granville" and west of Burrard to Stanley Park was "Liverpool". Granville was laid out with the long side of the block parallel to Burrard, whereas Liverpool had the short side parallel to Burrard. Pacific, Davie, Nelson and Robson more or less line up by accident. Granville was a CPR townsite and Georgia was already established as main street so the planners of Liverpool carried it through despite that it interrupts their grid, thus the narrowness of the block between Alberni and Georgia, the after-the-fact dog-legs at Smithe-Haro and Dunsmuir-Melville, the weird left-over street-to-nowhere that is Eveliegh, and all the other "what were they thinking?" weirdness that happens at Burrard.
And why does Burrard itself just suddenly end at 16th? Because, in 1886, that's where Vancouver ended. The original city limit was at 16th and all the space beyond was unincorporated nothing. When the Interurban electric railway was built between New Westminster and Vancouver the people that had land in the intervening unincorporated space got together to incorporate everything from Point Grey to North Road as a new municipality. There was a disagreement over the name. The farmers in the eastern part wanted it named "Burnaby" after Colonel Moody's secretary Robert Burnaby, who was the first to survey and map Burnaby Lake. Real estate speculators who wanted to make money selling lots near the Interurban line wanted to call the new municipality "South Vancouver" since they thought that was a more marketable name. They split the territory at what became Boundary Road. To the east was Burnaby, to the west was South Vancouver. South Vancouver incorporated in 1891. Burnaby in 1892. Like the Liverpool/Granville join, the grid for South Vancouver was laid out separately from the grid in Vancouver, thus the mis-match of Oak at 16th.
Because land was cheaper in South Vancouver than in Vancouver lots in the east were marketed to blue-collar sorts. The municipal government of South Vancouver refused to go into debt and roads and other services weren't getting built fast enough to suit the richer land-owners in the western part, so they split off (at Cambie Street, then called Bridge Street) in 1908 and formed the municipality of Point Grey. The abrupt change in zones on Granville at 16th is because at the time houses like Hycroft Mansion were being built, they weren't in Vancouver. Point Grey and South Vancouver were separate municipalities up until 1929, and it is no accident that the new (and current) Vancouver city hall, built shortly after amalgamation, is at 12th and Cambie, more or less where the three municipalities met.
So what's the connection to all this and that weird patch of nothing in the middle of Richmond? It goes back to the Interurban - and this is funny in a painfully stupid kind of way. The original line of the Interurban, built in 1891, connected New Westminster and Vancouver, spurring the creation of Burnaby and South Vancouver. In 1902 a second line was opened to Steveston. That's what the railway tracks beside Arbutus Street in Vancouver and along Shell Road in Richmond are. In the 1920's someone had the brilliant idea of putting an airport along the Interurban line in Richmond and that blot of nothing is it. When planes got bigger and longer runways were needed the airport was moved to Sea Island, but think about it for a second. In 1986, in order not to look like dufuses with the rest of the planet looking millions were spent to build the original line of SkyTrain between Vancouver and New Westminster. Guess what path it follows? The path of the electric railway that was there in 1891. And right now, again simply to not look like dufuses with the rest of the planet looking because of the 2010 Winter Olympics, hundreds of millions more are being spent to build rail transit to Richmond that we had in 1902 and a connection to the airport that we effectively had before there was an airport. It seems that in the area of transit all we've managed to accomplish in the last twenty-one years is flail around trying to rebuild what was in place over a century ago.