How can you believe that tipping is “out of hand”, but at the same time not care that many of us choose to tip?
I’ve never once tipped because I felt that I was compelled to do so.
If you don’t want to tip, don’t.
Being fit will only help any athletic activity. That said, if you are sore, muscles tight or recovering might have an impact on your swing. Getting a stronger body might change how the swing feels and you might have changed the swing unconsciously.
Having more flexibility should improve your swing until you allow the range of motion to take you out of good positions. If you have more flexibility but it isn't in the right proportions you could be making a longer swing but one that is now out of balance.
No way to know why without a swing video.