Hello! I am also having the same question as @LamCake, and I might be able to provide some context as to why navigating from the profile page is easier. We have over 300 students in our course, and they are divided into different sections, each with a TA. When a student goes to the People page, they see ALL the folks enrolled in the course, not just their section. As far as I can tell, there is no way to sort by section or TA, so they just have to scroll through the list to find their TA's name.
If we post the TAs names for each section as a list on the course website, with a link to the TAs profile, it is really easy for a student to know who to click on, and then be able to message from there. There are work arounds, but just wondering why no option to contact from the TA or teachers profile?