I haven't played blight yet, but noticed that exalts got quite cheap in one week compared to past leagues. Why is that so?

Exalt is ~~150 while it was ~~120 in the two previous leagues - first week.
Each new league markets are becoming more and more reactive.

But maybe you are talking about HC or Console ?

To be honest, I remember buying exalts like 250-ish+ after 1 week in legion (if im not mistaken :))

You are because exalt price is changing during the league: usually there's 3 phases:
1/ price increase to a maximum first weeks. ex: 30 to 180 chaos.
2/ pike and then flat or bit unstable for several weeks. ex: 180 +/- 20
3/ price adjusting following standard values: 160