Yes there is a point, I regularly pull through my engine (90hp) before start - always before the first start of the day when all is cold and quite often otherwise.
What are the advantages? First, if you do it regularly, it is possible to detect a difference
All very fine if you own your own aircraft, and know each tick, click, buzz and rattle and roll intimately. But try that with a flying school aircraft and then write up the various tick,click, buzz and rattle and roll in the maintenance document - and you haven't even flown the plane yet and you can guarantee the flying school will tell you to go fly someone else's banger but not theirs.
The manufacturer's Pilot Information Manual gives you all the minimum required information to operate the aircraft safely and you will notice nowhere does it mention carefully turning the prop to check the compression in each cylinder or priming the engine before hand turning the prop to make starting easier. And never rely entirely on the advice from instructors at any flying school. They may look cool in their pilot suits with bars and wings and big watches but the majority are hardly out of flying school themselves and all they know is what their instructor told them and so on.