Just because a substance has impressive specific strength, doesn't mean it has all the properties needed to make it generally useful.
Specific strength, the ratio of strength to weight, is a very important figure of merit for a material since it determines a number of theoretical limits. However, this totally fails to take into account other neccessary properties for a material suitable for more general use. A material should typically also be rigid, be practical to apply loads to evenly, not be subject to fatigue or hidden cracks, not be brittle or subject to catastrophic failure, and should have strength in the directions desired which depends on the application, but always some strength in each direction is desired for rigid components.
A material also needs to be affordable both to produce and to form or machine to the desired shape, and be resistant to the environmental conditions it will experience. While space programs expect and operate with large budgets, they do want to choose a less expensive option even if it is technically not the "best" one.
Ductile metals (steel, aluminum, titanium, etc) have many of the above desired features as well as fairly good specific strength, so they are extremely popular. Historically, the useful advance has often been fabrication techniques rather than fundamental materials, such as careful machining or 3D printing that allows a large, complex part to be made of a single piece of material with skins, structural members, and mounting brackets all combined and no wasted weight.
The Aerospace world is very conservative, even the mavericks like SpaceX.
Simply put, the world of aerospace engineering does not react to trends in technology very quickly at all, and especially not at the rate of hype and rumor. Aerospace projects often take years from beginning of design to completion, and safety concerns and the need for very expensive projects to succeed the first time mean that if an old technology works, a new technology will only be used if it provides a huge benefit or makes something possible or economically feasible that wasn't before.
While SpaceX has been less conservative in a number of respects than the "old guard" aerospace contractors and space agency staff who have historically designed rockets, that doesn't mean they aren't bound by the same conservatism for the same reasons, and moreover SpaceX has often followed the principle of using inexpensive, simple technology where possible to save costs -- for example, making Starship out of ordinary high strength stainless steel.
We're Kind Of Already Using It
Graphene refers to a single sheet of the graphite crystal. Carbon fiber, such as is used in carbon fiber composites, is made of carbon. Depending on the type of carbon fiber, a significant portion of the carbon is indeed in the form of graphene! While carbon fiber composites are a pretty good material and are used in a number of aerospace applications, they have limitations that mean they aren't particularly heavily used in space. Notably, Rocket Lab's Electron uses carbon fiber composite for the main body of the rocket.
Super-Specific-Strength materials tend to be specialized
Looking at Wikipedia's list of materials by specific strength, the highest specific strength materials (higher than ductile metals) listed include mostly:
- Fibrous materials, which will only produce cloth or rope by themselves (and whose strength is fundamentally tied to their fibrous form)
- Nanostructures that don't necessarily reflect a practical bulk material
- A wood that, while very strong and light, resembles styrofoam in its fragility and crushability.
Graphene is a fad (for right now)
Graphene has recently been developed to a form where lots of experimental applications can be tested, but people haven't yet figured out what it is good for in a really practical sense. This is accompanied with a great deal of hype. This is far from new: I remember when carbon nanotubes were the big thing, and occupied roughly the same position in hype. Hopes of space elevators and similar super-engineering were much depressed over time as nobody really succeeded in bonding individual carbon nanotubes into a rope or yarn with strength matching that of the individual tubes.