Does anyone actually believe that works have no place in the practice of faith?
Generally speaking, it has been my observation that all Christians believe that works are a component of faith, it's just that some do not realize it or are unwilling to admit it. The real debate comes down to exactly what sort of works are important. Ask any Christian (Catholic, Protestant or Orthodox) how one is saved and you will see that the description will inevitably include things that one must do. If we have to do something, then that is a "work."
For example, am I to accept Jesus as my personal Lord and Savior? If so, then "accepting Jesus" is the work I must do. Am I to believe in the promise of the gospels and put my trust in God? If so, then "believing" and "trusting" are the works I must do. Am I to be baptized? If so, then baptism is the work I must do. And so on and so on. Those who disagree with this either believe that everyone is automatically saved (which is contrary to what the Bible teaches about hell being populated) or they believe in predestination. Everyone else embraces the belief that we are to do some sort of work.
As a side note, someone once argued against my point by saying that a baby who dies has no way of doing any works. So let me clarify that I am speaking in terms of the "ordinary ways" in which we participate in God's plan of salvation. As the Church teaches, God operates in "extraordinary ways" as well, which we can realistically presume to include a plan of salvation for babies and people with mental handicaps who are prevented, by no fault of their own, from performing the works generally associated with the practice of the Christian Faith.
The real issue that becomes a problem is the belief that by works we can merit our own salvation. This is what Catholics are often accused of, but it is not a true representation of Catholic belief. Rather, it is the sacrifice of Christ that provides salvation. But salvation is a gift of love, and therefore we must be free to accept or reject it. The good works described in the gospels, and the sacraments are examples of the "works" we can do to accept this gift, and participate in the grace it provides. Faith is a gift from God, but one we are expected to put into practice after having received it.
And just to make sure I am "on topic" here, let me add that when St. Paul refers to being freed from the works of the Law (in Ephesians and elsewhere), he is referring to the customary requirement for a Jew to observe the Law of Moses. The Catholic Church officially interprets which parts of the Law of Moses are still binding on Christians (example, you can have a ham sandwich but you must still follow the Ten Commandmants). But in any event, we are to acknowledge that salvation comes through Jesus Christ and not by the practice of the Law of Moses.
It is also worth noting that Ephesians does not say "through faith alone" but simply "through faith." The concept of adding "alone" to the text comes through the Protestant tradition.