For a number of reasons our classes often train with wooden swords. Despite what you might think, very little of it has to do with the "safety"...
Wooden swords can be equally destructive as blunt-steel trainers. For comparison, imagine being struck in the face by a baseball bat; frankly it matters little whether the bat is constructed of solid oak or stainless steel. The two implements might ring your bell with a slightly different sound but as it happens, you still end up missing teeth.
Instead, our reasons behind the use of wooden swords are a bit more practical. The first of which is that swords made of wood are generally both more available and cost effective for keeping on hand as common shared gear. The low cost of purchase also allows for students to more quickly acquire their own tool for practicing both in and outside of class.
Second, these wooden swords are frankly more "sword-like". While they lack the flexibility of a steel sword, the shape and balance of these training devices is more appropriate to the Thrust and Slash (Stoß-und-Hieb) style of Longsword we study.
On a similar note, while the wooden swords are often a little lighter than many Feders (but not necessarily swords), newer students require time to build strength and flexibility before taking up steel. Attempting to wield a heavy implement without building strength leads to poor posture and grip, which in turn leads to a lack of control: a major culprit behind hitting or thrusting too hard. Building this level of control also leads to the ability to fence with a "light touch", and greater speeds.
Additionally, while the literal unbending nature of the wooden swords prohibits thrusting at full force, many of us would argue that this should also not be done with steel Feders, ask anyone who has received the all too common HEMA "waffling" why.
Third, even with the wonders of contemporary metallurgy steel training swords (colloquially, yet incorrectly, referred to as Federschwert or Feders) have a limited lifespan. With every instance of contact we chip away at that lifespan. This is in part due to the nature of the steels used to construct the swords, but also the method used to assemble them. Wooden swords have the nickname of waster because they are designed to get you through the common slog of training. There is no logical sense in beating up an expensive steel sword when a wooden one would do just as well.
A quick side note: breakage is in fact a positive quality of any contact-training tool. This means the implement is "absorbing" at least a good amount of force behind the blow. It's better to break a blade than your training or fencing partner.
Fourth, and most controversially, it is the opinion of many of our instructors that the blunt sword-like objects being used in contemporary HEMA tournaments are simply the wrong implement for use in a competitive environment and most training situations.
The Feders are poor analogs to their sword relatives, and frankly that's fine. For all intents and purposes they're not intended to be real swords; they are the implement of swordplay, yet modern Feders also fail in that arena as well. Even the most flexible and light Feder on the market requires such a cumbersome and stifling volume of protective equipment that they transform what should be fencing bouts into semi-armored MMA-style matches with the addition of a sword-shaped crowbar.
This is not to say that HEMA competitions or Feders themselves are bad or wrong (competitions can and should be rather fun!), but we must understand that these implements involved create a radically different context in terms of the application of the fencing arts. There seems to be a lack of introspection and outright refusal to blame the implement, these Feders, for a number of the issues experienced an tournaments that so many members of the HEMA-sphere are keen to point out; such as the lack of technique application, the inevitable deluge of injuries, particularly amongst smaller fighters, the application of excessive force, concussions, broken fingers, etc.,.
Obviously some of these issues are cultural problems that must be addressed socially in the training halls and at the tournaments themselves, but the physical object at the center of the activity should not be precluded from examination.
A prime example of this lack of reflective analysis is the never-ending-quest-for-perfect-gloves™. For years, HEMA practitioners have pursued adequate hand and finger protection that also allows for dexterous use of the sword. Mountains of research, labor, and money have been spent on attempting to build a modern "fencing gauntlet" appropriate for fencing with modern "Federschwerts". The results have been... varied.
The same spend-cycle has applied to modified fencing masks, jackets, and basically every piece of protective equipment from the exhaustively long list required to compete in a HEMA tournament. When the artful expression of fencing becomes radically more difficult or impossible to execute, at what point does one stop and think about ways to modify the fencing implement to allow for more a more adroit expression of the art?
To be clear, we do fence with Feders in our club. Likewise, many of us do have fun competing in a variety of tournaments with full understanding of what HEMA tournaments entail and how to specifically train for them. We also believe there to be better options available or just in reach of development (to be clear: not wooden swords) for tournament settings and we hope in the future to help contribute to that.
Wooden swords provide a practical way for our group to diversify our training; with an eye both towards the intended application of the tradition we study, as well as preparing us for the contemporary HEMA environment.