The first thing to consider is that (as of today) there is no general AI (AGI) and most if not all research don't try to create an AGI. An AGI can be described as an AI able to perform well (at least at a human-like level) on a wide range of tasks. If you are interested in the question I recommand you to do some research about the term AGI as there is no consensual definition, but I believe that the one I gave you will be enough here.
This means that an AI can actually do just one (or a few) task and so, if we created an AI creating new AIs it would just create new AIs better to either do something else (so there is no loop of improvement and it's not what you are interested in) or better to create a better version of themselves which in itself is useless as this better version can't do anything useful to us (except maybe to show that we can do it).
I don't know if there are examples of research creating an AI improving themselves, but there are examples of AI improving other AI such as this one where an evolutionary algorithm is used to design a better neural network.
Concerning your example about AI improving the hardware, it could indeed lead to the improvement of a wide range of AI, but it's, in my opinion, different than an AI improving themself as the loop take several years before being closed (from this source it take several years to produce a new cpu) where an AI directly training an AI could do so in a matter of days (or weeks or hours depending on the technology, but anyway it's way faster)
But, if we had an AGI able to create better, more or equally general AI, it could indeed lead to a breakthrough in AI*, or this is at least the opinion of some people including Nick Bostrom which wrote the famous book "superintelligence" in which he described how an AGI could very rapidly improve itself and described it as a possible singularity (meaning that we are unable to foresee what this AGI could become and how fast it could improve itself).
*at the condition that a better AGI is able to further improve the next version, which is not so obvious (thanks Neil Slater for this remark). Adding this condition it means that your metrics for "better" must include the ability to create a better AGI and that you can effectively always (or for long enough to obtain a breakthrough) improve this ability (As far as I know, we don't know if it's indeed the case)