I've had many boats and my current boat is the only one that came with a transom saver. Some of the older boats had some flex even with dry transoms - had one crack going across the Key Bridge where the road can cause violent oscillation. Mine connects to a slot in the trailer to the LU. The 1986 transom is more solid than other areas of the boat over the years. Transoms take a beating in the water but why add more of beating from our lousy roads. I'm nearing retirement and plan on keeping my 1986 since it's perfect for what I do on the water, so anything I can easily do to make it last longer than me is a good thing.
Outboard manufacturers want their motors in the running position when trailering, if the boat cannot be trailered with the motor in the running position , then a transom saver is recommended for trailering with the motor in any other position, you will find this info in your owners manual.
Yes the running position is a Must for the longevity of your transome. I see so many OB up whil;e running down the Highway and see them flexing. Even in the down position MANY boats would be just fine.