It would be a contraction of had: “I had better write…” Using would there doesn’t make sense. The function of had in the sentence is just to change the tense. Without had it’s something you should be doing now. With had, it’s something you should probably have already done.
It would be a contraction of had: “I had better write…” Using would there doesn’t make sense. The function of had in the sentence is just to change the tense. Without had it’s something you should be doing now. With had, it’s something you should probably have already done.
More or less my point, languages are weird with lots of arbitrary idiomatic things—‘would rather’ but ‘had better’.
After posting the comment I’ve thought ‘wait, it makes more sense for it to be should’ so my guesses are a bit off today.