In fact they already do. PCI express x1 is a single (bidirectional) serial link. x4 and x16 are multi-lane serial links, but it isn't correct to say that it is a 4- or 16- bit parallel link. The channels are largely independent at the electrical level (each channel generates its own recovered clock) and the controller stripes data byte-by-byte (not bit-by-bit) over the active channels.
Parallel buses are still the king for extremely high bandwidth, low latency, close range connections like on-chip data bus, a memory bus, or a ADC connection, but as soon as you want to transmit more than a few cm, it is time to serialize (if you want high speed).