There are several manufacturers that make available custom ordering. Many offer this customizing service right in the store.
You can find custom blinds that are made-to-measure/order with 2" slats. Natural bamboo blinds can run around $59.99. When you order them, they will be sized to the exact width and length you need.
The price may increase or decrease depending on the size needed.
4windows is a brand you can purchase online. Pricing starts at $24.33 for horizontal and $35.00 for vertical blinds. They're made from aluminum and can be ordered in 2", 1", or 0.5" slats with many different color choices.
Hunter Douglas also creates premium quality custom fit blinds. The EverWood X-tra Blinds with 2 1/2" slats and the look of a shutter but operate as a blind.
Some custom blinds may cost a bit more money than regular blinds but this is because they have to be individually and specially cut.
With the latest innovations in design and the cooperation of companies like the home depot and other home improvement stores purchasing equipment, blinds can be custom cut to your needs without costing you any more than the standard sizes.
Online stores can also customize them if you have the measurements of your window to give them.
The blinds themselves are built in such a way that the technician in the store can move a lever back, then cut off the excess length of the top and bottom halves of the blinds then they lock the mechanism piece in place, replace another piece for capping it off and the blinds are the exact length you need.
Some specialty blinds, for example, for rounded windows are also designed to be cut to shape and both halves re-assembled to fit any size needed.
Customization is a very necessary step in the industry.
The demand is matching the latest in architectural design and many renovating their home into a more modern look often will use the curved shapes instead of the static ones.
In many ways it's the same as how cars used to have square boxy headlights and now most cars have rounded and streamlined shapes (overall).