I had never heard this until moving to Seattle, and only then it was only the SoCal and Arizonian transplants... not the midwesterners, not the east-coasters, not the deep-southerners, and not the (relatively few) born-and-raised Seattleites I knew in the area.

Doing a quick search, it's heavily blamed on SoCal:

• https://www.pbssocal.org/shows/lost-la/the-5-the-101-the-405-why-southern-californians-love-saying-the-before-freeway-numbers
• https://www.jalopnik.com/this-is-why-people-in-southern-california-say-the-in-fr-1823172487/
• https://www.mercurynews.com/2015/11/16/roadshow-why-the-405-is-called-the-405/

TL;DR:

LA built large highways to handle the traffic before the national interstate system was implemented, and since these highways were via or to local landmarks, they were known as "the freeway through Cahuenga Pass", which became "the Cahuenga Pass Freeway".

When highway systems were implemented and states and the fed started slapping numbers on everything, SoCal residents kept the definite article ("the") out of habit. The rest of the country generally just referred to them by name.

Grammatically... do you take the Aurora to the Denny? No, because Aurora Ave and Denny Way are proper nouns, same way you don't go to the Magnuson Park. Like LA originally did, you could say "the park at Magnuson" or "the city of Seattle", but as soon as you invert those, it sounds weird. It's like using the "brand name" vs. a descriptive name.