The image in the original post is not something I would even call a "logo." It's graphics wrapped around a painted illustration. That sort of thing does not lend itself to being reproduced in small sizes, like in a little 1 column black and white newspaper ad.
I agree with the comments of others that not everything has to be vector-based. Nevertheless such artwork must be created in a sufficiently high level of native resolution to be useful in a variety of purposes. This sort of thing could be a mix of raster and vector (vectors for the type and raster for the illustration).
Still, such artwork limits the customer in some ways. You can't cut it out of single color of vinyl like you can with most true logos.
With logo design less is definitely more. When I design logos I always make the finished "master" version 100% vector-based. I also try to make it where it can be produced with a single color. Ultimately that can save the customer a lot of money on print costs and make the finished graphic far more versatile. It's very easy to take a vector-based image into Photoshop and cheese it up with all the bevels, drop shadows, lens flares and other junk. It's stupid to design a logo in Photoshop and then try to take it into the vector realm afterward. Sadly, so many amateur graphic designers passing themselves off as professionals keep doing it anyway.