I am not very familiar with the Multiple Intelligences, but I have encountered them in various ways over the years. The main way was through tests designed to indicate a career path. These kind of tests are great for indicating jobs that you might like.
Willingham has truly opened my eyes in a number of regards. The biggest eye-opener for me, which makes perfect sense, is that there is no evidence that applying modalities when teaching individuals based on their professed preference has any benefits.
I think the most important problem with modality approaches is the assumption that modality can be applied successfully based on the individual without regard to what is being taught. Teaching someone with a visual preference using a visual modality will not bear more fruit than the usual teaching techniques. Another problem is that modality approaches assume that children learn best in only one way, and that we have to specialize instruction for each individual student. Willingham's research has debunked this myth, perhaps.
Instead, the modalities are most usefully applied in the classroom as supplemental materials. They are more useful for livening up the class than for teaching specific individuals. With regard to workload, this should make teachers happy. It means that rather than spending inordinate amounts of time per student, they can create their lesson plan for the entire class, with a minimal focus on specific students 'learning styles.' In other words, only the students who truly need special circumstances will require that preparation.
What we've learned from Willingham is that modality can be used in the classroom to liven up the material in general. Certain subjects will lend themselves to certain modalities more readily than others. For example, music appreciation is primarily taught by listening, although basic music theory can be illustrated on the board as well. However, since "Children are more alike than different in terms of how they think and learn," it isn't necessary for modality thinking to dominate the classroom. (Willingham, page 113)
Other subjects can be taught in a variety of modalities which can make the subject matter more interesting and applicable for the students. Altogether, it is perhaps best to use modalities in a holistic manner. They should be integrated with the standard curriculum as supplemental materials in order to maximize their usefulness. I think that it isn't necessary to use modalities in instruction, but I also think that the students would be appreciative of their inclusion, even if kept to a minor role in the classroom.
Why Don't Students Like School?, Willingham, Daniel T., Jossey-Bass, 2009