What's the point of omitting the "e", as in "sceptered" going to "scepter'd", in English poetry?

This was to signify that the syllable was omitted. In most cases today, we don't pronounce the final syllable in many -ed endings that used to always be articulated. You can see a remnant of this in the word learned: We say that word in one syllable in the sentence

I learned a lot from him.

but pronounce it as two syllables in

He was a very learned individual.

The idea of the apostrophe was to show that the syllable was being left out so that the line would scan correctly. In the first line of your example, pronouncing the final syllable -ed *inspired* would ruin the iambic pentameter and leave the last syllable unstressed.

At one time, inspired would have been pronounced as in•spi•red, and sceptered would have been scep•ter•ed. Shakespeare, Tennyson, and other poets were just making sure their verses would scan for the reader.