Syllables. Doesn't anyone count syllables anymore?
Listen.
And the rockets red glare.
(six syllables. Add--> "rockets red glaring" an arcane image even unto today.)
And the bombs bursting in air,
(Clear image but seven syllables)

The word "and" was needed as a mnemonic but had to go, so "the" was left to supply the requisite syllable. But when singing, without the mnemonic "and", people forgot the line and so paused until some smart fellow said "the Bombs ...". More and more people waited to hear "bombs" and so by default the "the" was eventually left out. Leaving one pause and five syllables.
That odd conditioned pause is what wof's ears remember.

I think,
milo.