We don't use any helping verb after "as soon as" but we use hv after no sooner at first in a sentence, so what is the sensible reason behind it

English has a sort of construction where a negative adverb modifies the clause, and triggers "verb-second" word order. What that means is this: That adverb goes at the start of the clause where the subject would normally go; and the verb goes second. Questions with a wh- word trigger verb-second word order, too. So: negative sentences:

1a. No sooner had I reached the station than the train left.

1b. Never have I seen such a thing before.

1c. Nowhere is this more common than...

Questions (I give these to give another context with verb-second word order.)

2a. When did you reach the station?

2b. When have you seen such a thing before?

2c. Where is this most common?

Verb-second word order can also be triggered by some adverbs which aren't actually negative but have some negative aspect in what they mean. For example, seldom. But it doesn't happen with positive adverbs unless the writer's being old-fashioned or poetic (Often have I...).