The only problem with this approach is the amount of time before your interest in a new thing starts to fade is often just about the same amount of time it take

The only problem with this approach is the amount of time before your interest in a new thing starts to fade is often just about the same amount of time it takes to recognize the limits of the cheap stuff and decide to upgrade. It's definitely happened to me multiple times. And I don't think it's just a coincidence, with any new hobby or skill you will start out improving very quickly and then eventually hit a plateau. The first thing you think when you hit the plateau is "I would be a little bit better/have a little bit more fun with this if I had better gear", and it's usually true and you do get a slight boost. But then a little while after that you hit a sustained plateau anyway and that's the point where you'll often lose interest.