Why does a run of 4 in Cribbage score only 4?
First off, taken one way this might be an unanswerable question

I'm struggling with the question. It seems to be asking folks to guess on what they think the rationale might have been for scoring 4-card runs as 4-points instead of 6 (or some other number); however, since the game was invented in the 17th century its inventor is long-since dead, and absent some comprehensive history on the game and its inception that I'm not aware of the real answer to the question is not knowable. In other words, we can come up with some reasons that seem logical to us, but we will probably never understand the thought process of the game's inventor. 

That said, here's why I like the rule as-is (and incidentally I like your question because I've had the same thought):

The best possible hand in cribbage is 29, which involves the Jack that counts for nobs and all of the 5s. Now although hands with lots of fives are always good, often retaining just one or two will only result in a mediocre score where you count a few 15s, a pair, and are done.

In contrast, a strategy that relies on runs, pairs, and 15s will have a lower maximum score, but will get more points if the up card is not exactly as desired. 

For example if you're drawing for the best possible hand failing to get that last 5 as the up card will cost you 14 points, as you'll only score 15-8, a pair royal for 6 and 1 for his nobs for 15.

Consider now the runs, pairs, and 15s strategy, say for example, 6-7-7-8-9. Based on the rules this hand scores: 15-2 (7-8), 15-4 (7-8), 15-6 (6-9), run for 10 (6-7-8-9), run for 14 (6-7-8-9), and pair for 16 (7-7). A super solid hand. In the previous example there is only one card in the deck that gets you the extra 14 points. In this hand the best draw is one of the 4 nines, but the drop-off in points isn't that much if you draw another 8, or a 7, or a 6, or a 5. Less upside potential, but a much more robust hand statistically speaking.

Now here's why scoring runs differently breaks things.

If runs of 4 were scored as 6--or more precisely, if you got to count for 3 points every unique run of 3 that you could make, this hand scores much higher. The count to 15-6 is unchanged, but then: run for 9 (6-7-8), run for 12 (6-7-8), run for 15 (7-8-9), run for 18 (7-8-9), pair for 20 (7-7). Or perhaps a much simpler but more dramatic example is a hand of 5-6-7-8-9, where the score for just the runs would go from 5 points to 9.

If the value of runs is increased, this incentivises players to only go for the much more likely (and now also relatively more lucrative) run hands instead of the larger payoff but higher risk 15 hands. This would make the strategy of the game more myopic and because everyone would be playing the same way because the relative payoff of going for the knock-out blow would be much reduced.

I don't want to make too much of all this (too late probably) because ultimately a players freedom is highly restricted by their cards (you only get to discard 2 after all), but the incentives of changing the rule appear to be to be tilted in the wrong direction.