I've been doing contract work for over fifteen years, and the only contracts i've signed have been employment contracts with agencies, but never when I negotiate directly with the actual client. Most small businesses are very uncomfortable with lawyers. It can easily add thousands of dollars to a project, and for most small businesses, it is not worth it.
If you are doing business with an unknown agency in a far-flung place on the planet with someone who isn't going to be paying your invoice, or accepting it for approval, for a project that is in the mid-five figures or more, you certainly want a contract to back up a detailed spec.
But if you are doing a $1500 project for a business in your own town, that you can go to their offices, or they can pick up the phone and call you, the request to bring a in a laywer will understandably frighten most potential clients away, since it could add a thousand dollars or more to the deal. Plus, most business people try to avoid lawyers whenever possible. Most businesses that have been around for a while know that they don't want to burn a good developer or contractor. Not only is it a PITA to find such people, but they know word gets out.
Saying, "I'm going to charge you a lot of money if you don't pay on this date" is not a very good way of building up a good business relationship.
Disagreements on deliverables is best done with specificity at the time of the problem, in a co-operative, problem-solving mode, not in the adversarial mode that lawyers and contracts create.
If you get a deadbeat client (in my experience - very rare and easy to spot) having spent money on a lawyer to draw up a contract won't get them to cough up your money, it's just letting good money follow bad.
On the other hand, if they have in-house counsel and routinely require contracts, it's fine to sign it. Just be sure to take it home and read and understand it first, and keep a copy for yourself. Most contracts offered are very one-sided, so you want to make sure that your interests are protected. If you want to get a lawyer to explain it to you, it will cost you a lot of money. You could find one-sided contracts offered by contracting agencies to their clients to see what your side should be looking at and make the modifications and negotiate the contract.