You might get away with just using flat counters in the case of stand-based units. However, consider what happens when using flat tokens for individual minis. Even in 28mm scale, this means 1" circles or squares where you should fit enough information to represent the unit. For games like Song of Blades and Heroes (SBH) or All Things Zombie, that might be feasible: a flat token with a unit portrait and the few relevant stats, possibly a letter or number to identify similar creatures. Now move down to 15mm gaming. 10-15mm squares with text in it will be hard to read, whereas even a simple paper figure might make it easier to identify.
Now, to be clear, the artistic pursuit of creating paper minis as close to their resin and metal counterparts is very interesting. However, when considering practical factors and the "figure as game token" approach, other alternatives should not be ignored. In the following picture I have placed a few different paper miniature building styles. From left to right we have: two minis cut close to the outlines, and glued to plastic bases; two more cut close to the outlines with octogonal paper bases; three figures in "inverted T" style with textured bases; three in "A-frame" style and two 28mm-scale "inverted T" figures.
There is no discussion that the figures cut close to the outlines look better but in my experience, the others can be built a lot faster, making them ideal, at the very least, for trying new games. Although in that picture all the minis have white backgrounds, light colors could have been used to color-code different armies or unit types, adding information to the game token. Likewise, although these figures have front and back images, one might have symbols or small amounts of text on the back of each figure. Note: I'm not including the "triagonal" format in this discussion because I find it awkward to use in miniature games that require that minis have a defined front facing.
There is another aspect that differentiates paper miniatures meant to be cut close to the outlines from the ones to be used as "inverted T", A-frame etc.: perspective. Normally, the front and back views of the same figure will have different outlines thanks to the effects of perspective (i.e. foreshortening.) A nice example can be seen in this barbarian figure from Arion Games -- just check the hammer he is wielding.
Now, if you want a mini that can be cut along the outlines, you need the front and back to match. The only ways this will happen are:
a) all elements are placed (approximately) at the plane of the image, i.e. nothing jutting out or extending towards the back;
b) your image uses parallel projection, i.e. no distortion due to the distance.
The effect of doing either is that you lose some depth and dynamics from the figure. Comic book authors tend to exaggerate perspective effects because it adds movement to the image. Now, if your paper figures don't have to have matching front and back outlines, there is no such limitation. As a bonus, you can have figures in poses that would be too complicated to cut out otherwise. This also means that publishers who use inverted T, A-frame or triagonal formats and don't exploit different poses and perspective are really missing out on the opportunity.
Although I find A-frames less attractive than inverted Ts, they also have two interesting qualities. First, because the images are placed at angled planes, they are readable even from a steeper angle. Second, they actually enclose a volume, so they don't feel as "flat" as other paper minis. Some people will value these features higher than others, certainly.
To finish this crazy rant, I have two images to illustrate the use of inverted T's and A-frames. First, here's a picture of some insurgents vs. soldiers.
Second, here's "Get to the flying thingy before the bugs overrun us!" -- soon to be actually played out using the old BUGS! rule set from Two Hour Wargames...
Each picture was taken at about 50cm away from the table. What I wanted to highlight with them was the readability of the different figures on the tabletop. While these aren't pretty dioramas, it is possible to distinguish the figures and what's going on.
I've spent a considerable amount of time making paper figures and terrain but recently I'm starting to think about them as game tokens, so their practical use takes precedence over visual impact. Some times you want a gorgeous table, other times you just want to play the game. This doesn't mean I'll stop making more elaborate paper figures; it's just a change in priorites.