Arenas are a similar concept that work well in non-GC environments if you don't let objects allocated during a request escape to live beyond the request.
Thread-local pools to satisfy allocations are also a well-known technique used in various allocators so your system's malloc might be doing this for you. It might also be able to efficiently collapse free lists which more or less behaves like an arena allocator when your request pipeline doesn't let allocations escape.
In practical terms: most approaches generalize well enough that if you follow the rules you'd need to follow anyway you get the benefits without the drawbacks. In most of the remaining edge cases you get even better benefits by adopting other strategies. For example Unity uses C# which has a GC... but games shouldn't allocate on the game loop _anyway_ so GC vs ref counts vs malloc isn't very important compared to avoiding allocations altogether. Or if you already obey the rules you'd need for an arena allocator in your server then letting the GC or allocator deal with it might mean you can coalesce cleanup across multiple requests which may actually be better for performance anyway. And without manual arena management you don't risk problems if some esoteric edge case in the code needs to allocate something that will outlive that specific request.
There's nothing really stopping systems from exposing a hint for controlling this, but usually the people who might care about it don't just want hints, but actual guarantees, and then you have to consider all the users who hint incorrectly (or correctly, but for a different system/version). So, the benefit/cost ratio is low.
Integration of GC with thread scheduling was once an active area of research, but the world has mostly moved on (perhaps prematurely, but so goes).
"just increase the pointer" is a bump allocator.
An arena can be used with any allocator, not just bump allocators.
Arenas allow you to not worry about freeing memory, since it will all be freed in a single chunk. It also allows using allocators which are less concerned with fragmentation, since it is known that the arena memory will eventually be dropped.
The amount you are concerned with fragmentation ranges from zero concern (bump allocator) to moderate concern (maybe buddy allocator) to larger concern depends on the application and its tradeoffs, like most things in software engineering.
E.g. a http server just processed a request and sent a response. Before it sits in the queue to pick up a next request, it could tell: Now is a great time to stop this thread if you really need to. Ditto a GUI processed an event.
GC could do a minor collection there. Malloc/free could take or give back some chunks to a lower level or the OS.
Java had System.gc() but it was more a 'take as much time as you want on every thread and go deep'. I am thinking more of 'Here is avtime limit of a few ms, reorganize this thread only'.