The STP08 only has +/- 8% matching... I doubt he would see more variation than that anyway, if he buys all the LEDs at once.
He can tweak the LED supply voltage to get the current right.
The 8% is the worst case on one specific drive level that he would not be using. At the level he would be using, it's 3% max, 1.5% typical. An LED is going to have a LOT more variation in Vf than that, even just due to temperature variation - no way is he going to get close to 3% or even 8% with voltage tweaking. Looking at a typical 5mm Avago LED, the Vf shift is about 0.1 volt per 20 degrees. He'll want to do as little dissipation as possible, so if the Vf of his LED's is 1.9@10mA and he wants to string 6 of them in series (just as an example), and run them off 12V... that's a 60 ohm resistor. Over a temperature change of 20 degrees, that's 0.1V per LED which doubles his current to 20mA - a huge difference. And it doesn't account for inherent differences in LED forward voltage from manufacturing. Sure, you can tweak each string and pick resistors for each if you want - but who has time or motivation for that? But the light output difference between 10 and 20mA will be significant.
The cheapest STP08 part I see at farnell.com is STP08DP05XTTR for $0.75 qty 100 (and it's UK stock).
Meanwhile, 74HC595s are $0.10 at Arrow, qty 1.
STP08DP05MTR - 28p (about $0.44)/100. Or no reason not to go with the 16 channel version like STP16 or similar for 60-70 cents/ea @ Verical/Mouser/Digikey... then he only needs 25 of 'em. Or if price is an issue, they can be had for 30 cents/ea w/free shipping on eBay. And not to be pedantic, but just to be pedantic

the 74HC595 is $0.10 for 50pcs - and that's actually a really good price, I checked Octopart and for some reason Arrow doesn't show up - next best price I see is Avnet $0.26/50. Lesson learned - always check the distributors directly before trusting Octopart or Findchips.
Hey, I'm not saying the CC shift register is going to be cheaper than a 74HC595... but it seems a really small price difference (what, a few bucks?) for doing it the right way with several added benefits to boot.