Depends on the kernel.
Even Kernel 5.10, which is LTS, had a lot of issues upon full release. I use release candidate kernels sometimes because I use newer GPUs and CPUs, and they were more stable on some RC kernels. Depends on hardware and what they introduced into or fixed in the kernels. Not every new kernel is the same.
Depends on hardware. If you have a newer GPU, say Radeon Navi or GTX 2000s and newer, it might be better to stay on newer kernels. AMD GPUs does better with newer kernels (depending on the GPU), because all the open source drivers are built into the kernel itself and newer kernels sometimes have a lot of fixes for those GPUs. Not to mention a lot of fixes for newer CPUs as well such as newer Ryzen CPUs. Some stuff are backported or older kernels, but not everything.
Also, not every newer kernel fixes issues with specific hardware / software. Phoronix does pretty good explanations on what each new kernels introduce / fixes.
i.e. Linux 5.11 per Phoronix. Note: this is from December 2020, there were more fixes and stuff if you read the newer updates.
I had my Radeon RX 5700xt since kernel 5.5, and my gaming experience has gotten better as newer kernels got released. This is anecdotal for my specific hardware.
Could? Of course! But not always. Depends on your specific hardware and software setup, and how it interacts with the newer kernel. I had a ton of compatibility issues with my 5700xt originally, and some of the newer kernels fixed them!
Some kernels have progression with specific hardware, some kernels have regressions for specific hardware.