It matters because the agreement is not paperwork that follows the work — it precedes it. Providing services to a healthcare client without one signed is itself a breach of the rules, separately from anything going wrong, and it is the kind of failure that is trivially easy to prove after the fact.
The common trap is treating it as the client's document to produce. Many smaller practices have never seen one and will happily let you start on Monday; a hospital will send you theirs and expect you to have read it. Either way the exposure is yours, and "they never asked" is not a position you want to be explaining.