You can picture hasten as a person suddenly walking faster towards somewhere they need to be - the pace picks up, and the place they are heading for is already in view. Everything else the verb does keeps that quickened pace and changes what is being quickened. First it is your feet. Then it is your mouth, when you get a sentence out at once instead of waiting. Then it is something outside you altogether: an ending, a decision, a recovery, pulled forward in time.
From the word’s history
Hasten was formed from the noun haste plus the verb ending -en, and it started life as an intransitive verb - that is, as somebody moving in haste, with no object after it. The 'make something else happen faster' use, which is the one most readers meet today, came from that older picture of a person hurrying.
hasten 是 haste（匆忙）加上動詞字尾 -en 造出來的，最早是不及物動詞，後面不接受詞：講的就是人自己在趕。今天最常見的「讓別的事情變快」是從那個「人在趕路」的畫面延伸出來的。
Wiktionary entry for hasten, supplied in the evidence packet (source_ref kaikki:3f6f69a190036ae4:440247181:20998): 'Originally intransitive, from haste + -en (verbal suffix).'
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