Only Tonto from The Lone Ranger would word the English sentence this way.
"There are very many ancient streets in Rome" would sound much more natural.
How does one determine that "antiquae" modifies "plateae", rather than "Romae"?
I would think that it is a bit of a word order here. Latins word order is relatively free... but only relatively. Sooo that is my guess..
You could use "plentiful" to sound more natural in English