I have never noticed the SpaceX rocket launch videos include a timeline.
This image is from the Falcon Heavy launch with the Tesla car in it.
SpaceX regularly includes a timeline of noteworthy mission events in their live streams.
One of the founding principals of SpaceX was a desire to inspire humanity to be excited about space travel again. Educating and explaining as you demonstrate is one good way to get people more engaged and interested.
I also get a strong impression that Elon Musk and his employees seem to really get a kick out of what they are doing, and showing it off to the world (with details) is a natural response to that.
Graphic overlays on live video are easier and more common now. So it may simply be, "because we can".
Furthermore, there are business reasons for making launch videos more interesting and widely available:
Private launch companies have the need to make their communication more sales friendly to attract customers.
Interesting communication helps recruit talent.
To educate the general public about private rocketry. Prior to this decade, most people were only aware of NASA or Russian government launches. Since much business comes from government contracts, maintaining good public perception, with things like cool launch/landing videos, is good business.
The timeline is new, but the information it conveys has always been part of launch broadcasts. In older launch broadcasts, the timeline was not shown on-screen, but the items in the timeline were called out by the presenter (Apollo 11 example). The broadcast includes a few information overlays (e.g. countdown and launch time).
These days, it's much easier (=cheaper) to produce such graphics than it was in the 1960s.
On Ariane 5 launches, the webcast includes a graphic of the go/no go status:
The Still Testing flight of Electron by Rocket Lab in January 2018 also included such a graphic in its live online broadcast.
The graphic included
terminal countdown (start)
The removal of a commentator announcement at crucial times means audio feed can be directly from the control room (as done in the broadcast) allowing viewers to experience "behind the scenes" action and remain aware of progress during the flight.
For Rocket Lab, this is more important given their profile, but growth of public awareness is significant to any business. The more a person knows, the more they are likely to want to know, and to become involved in finding out.