The answer is most always “Yes”. Actually, I can’t think of any situation where you wouldn’t want a gate on both sides if it is possible. Sure, a gate may add a few dollars to the overall cost of the fence project, but will pay off greatly in reduced aggravation.
Picture yourself playing catch with your child in your back yard, on the side of the house that does not have the gate. Your kid throws better than you think and the ball sails over the fence. Guess how far you have to travel to retrieve that ball. You got it, all the way around the house to get to the other side of the fence. It grows old, fast. You will soon forget the bit extra paid, but will thank yourself for that gate every time you go through it.
The same goes for when you are doing your flower beds and yard work. Instead of wasting time trotting all the way around, you simply nip through your gate.
As far as that extra cost goes, your fencing contractor may just throw it in, if your project is large enough.