Private jets allow them traveling without the inconvenience of other people. Mega yatchs allow them having a private hotel that follows them as they travel.
A mega wealthy person has a busy schedule meeting with other elites, and they will often want to do that with maximum comfort and privacy. As long as the schedule isn't too tight, their crew can guarantee that the yatch will be there for them when they arrive, without the risk of having to see or be seen by lesser people.
The fact that the immense majority of people can't do the same is just the icing on the cake.
Paul Allen's Octopus was so much more:
[1] https://en.wikipedia.org/wiki/Octopus_(yacht)
[2] https://www.boatinternational.com/yachts/editorial-features/...
So he spent 0.1% of his wealth on this! Pretty reasonable budget to spend on something you enjoy IMHO.
He also put it to use on some exploratory missions, rescue mission etc.
For comparison, if your net worth is $500k, that's like spending $500 on something.