Greens are DPSS because they are the easiest color to make with DPSS crystals. In fact, it's so simple that somebody grew their own crystals at home (with no fancy lab fabrication materials/techniques), shined an infrared diode through them, and got a decent amount of green out.
Further, the technology required to make red and infrared diodes has been around far longer than any others. It's a different kind of semiconductor used to make diodes of less than around 600nm (or something). So, when those diodes first came out, and someone wanted a visible laser (i.e. green), they had to use what they had - red/infrared diodes. So, they figured out DPSS long before they managed to make 405nm diodes.
Because that process has been around for so long, it's become absurdly cheap since it has become optimized. On the other hand, 520nm diodes only recently came out (within the last year or two) and so, while they will probably eventually become as ubiquitous as the 445nm diodes, it'll take some time. Right now, they are really only available to buy in mass quantities, directly from the company. We get them from middleman companies who buy directly from the companies.
Further, for other color diodes, yes, they do exist. There are diodes around 473nm, 488nm, there have been experiments in laser diodes emitting around 610nm, but for laser diodes emitting in the mid-high 500nm ranges, none exist as yet I know. The technology just hasn't been developed yet. It requires a completely new type of semiconductor, which means it would probably take millions in research just to develop it... and it would have no use.