Mark,
I think there are several reasons;
1) An effort to have "sufficient" total card yardage to be seen as a significant test.
2) Particularly on heavily played public courses, the idea that smallish greens do not hold up to foot traffic well.
3) Where do you put the requisite 5 sets of tees when the tips are 130 yards?
4) The modern philsophy that suggests that these holes have more in common with "pitch and putt" than "real" golf courses.
As far as your question whether all golf holes are designed this way, or just par threes, I have to say that although most of the earliest short par threes had tiny greens, the example of the 6th at NGLA is anything but. And, not all holes are designed to some formula of approach shot to green size or exactness, particularly on the best courses.
However, what I'm seeing more and more of on modern courses is that most every green is within a certain size range, irrespective of the demands of the approach.
I'll give you an example, based on the course I played yesterday;
1) 375 yds, 30 deep, 37 wide
2) 365 yds, 33 deep, 36 wide
3) 435 yds, 38 deep, 26 wide
4) 462 yds, 30 deep, 28 wide (interestingly the smallest green on the course to this par four)
5) 603 yds, 27 deep, 35 wide
6) 223 yds, 36 deep, 36 wide
7) 538 yds, 32 deep, 36 wide
161 yds, 27 deep, 33 wide
9) 392 yds, 36 deep, 33 wide
10) 410 yds, 30 deep, 26 wide
11) 190 yds, 27 deep, 35 wide
12) 320 yds, 33 deep, 30 wide
13) 534 yds, 37 deep, 22 wide (widest variance in shape)
14) 425 yds, 32 deep, 33 wide
15) 195 yds, 34 deep, 34 wide
16) 515 yds, 33 deep, 36 wide
17) 415 yds, 38 deep, 32 wide
18) 425 yds, 39 deep, 36 wide