hi,

I thought about such way. For example, Allegro Micro has produced A6275/A6277 (8 bit), A6276 (16 bit) devices which provide constant sink current.
But next warning keeps me away from usage of them:

<< These devices are designed to operate with driver voltage drops of 0.4 V to 0.7 V with LED forward voltages of 1.2 V to 4.0 V. If higher voltages are dropped across the driver, package power dissipation will be increased significantly.

To minimize package power dissipation, it is recommended to use the lowest possible load supply voltage or to set any series dropping voltage (resistors) or a Zener diode, or a series string of diodes (approximately 0.7 V per diode) for a group of drivers.

For reference, typical LED forward voltages are:
White 3.5 – 4.0 V
Blue 3.0 – 4.0 V
Green 1.8 – 2.2 V
Yellow 2.0 – 2.1 V
Amber 1.9 – 2.65 V
Red 1.6 – 2.25 V
Infrared 1.2 – 1.5 V
>>

For me, it sounds like I need some additional hardware to provide requested voltage. In case when I have different LEDs (for example, set of blue, yellow and green) I need either with different voltage supplies or with different resistors/number of series diodes. I dont know - for me it seems more easy to use just different resistors with standard drivers like 6B595 and so keep power dissipation at resistors.

Anyway, it is question of own taste.

Regards,
Oleg