The downside (if there needs to be one) as it relates to your vehicle, dog and yourself is the eventual mess that builds-up as a result of transporting your dog. Even with dog covers neatly placed in the vehicle, both dog hair, slobber and dander tend to make their respective way all over your vehicle in do time.
As a result, the by-product of transporting your pet tends to accentuate the level of dirtiness in the vehicle overtime.
If your able and/or willing to do the upkeep on the interior cleaning portion of your vehicle, regular monthly vacuuming is recommend. This serves to keep your pet's dirty by-products (sand/grit, hair and dander) at bay.
Additionally, dog slobber if left for a period of time can stain the fabric on your vehicle's seats. This is unfortunately a very difficult stain to remove properly either via all-purpose cleaner and/or a combination of steam-cleaning.
The moral of this post, enjoy your dog, the outdoors and if your using your vehicle to accomplish this, keep its interior cleaning regiment in check as well.