But we're not moving through the park when we exercise (at least, not necessarily) Just as in English we could say "I jog/run/walk/cycle through the park every morning." but not swap in "exercise" or "play football", which are things you generally do at/in the park.
Think of this を as not marking the location so much as the route.
These are all possible, grammatically:
公園で散歩する = take a walk at/in (within the confines of) the park
公園を散歩する = take a walk through the park (more natural than the above?)
公園に散歩しに行く = go to the park for a walk