Though this may sound like a great option, most women are more romantic than this. Personally, an engagement only serves two purposes: to have time to plan a wedding (which is a big one for girls), and in the mean time, to make your intentions known that you're committed to that other person for the long haul.
Weddings and engagements aren't typically for the guy. They're for the girl so don't ruin the dreams she's had since she was a little girl just because you're too lazy or don't want to put in the extra effort and/or cash to do so.
And engagement is still an important part of the process. Don't skip it.
I wanted to elope and my wife was 100% on board, until she really thought about wanting her dad to walk her down the aisle.
It is NEVER about the groom. Ever. Even after you're married