We don't need globs of fat all the time but in practice some problems emerge if we go too low. Fat aids protein digestion and slows starch uptake (usually a good thing) and it's an indivisible part of liver, egg yolks, omega-3 fish, etc. SFA intake also plays an important role in HDL and certain hormone synthesis.
Overall I'd focus on the "nothing too drastic" part and make the obvious cuts like creamy desserts and beverages, oil dressings, and the like.
Lots of: urban hiking, cycling, sprinting
Lots of: fresh meat, seafood, eggs, organs, tubers, starch fruits, vegetables, meat fat, dairy fat, oil fruits
Some: cured meat, dairy protein, sweet fruits, rice, pulses, tree nuts, oil seeds
Minimal: soy, refined proteins, sugar, liquid carbohydrate, grains, refined oils, peanuts