Do you honestly think that we would have near the things we have today if not for patents? Do you really think some hobbyists were going to invent the transistor, the microchip, the complicated and expensive processes and tooling for manufacturing ever smaller and more powerful chips, battery technology, touch screens, all the lightweight but strong materials we have, LEDs, whatever? If so, you are seriously deluding yourself.
Patents have existed for only a few hundred years. People have existed for thousands of times longer. Why were the ancient Babylonians not walking around with cell phones? Why did Da Vinci's inventions only exist as drawings, and not practical things? How were we able to go from communicating only by sending letters to being able to to see and talk to someone anywhere on Earth with a small handheld device that weighs a few ounces? Could any of those things have to do with having a financial incentive to work on them? Just maybe?
Nobody says that patents are REQUIRED for innovation to occur. The purpose of patents is to PROMOTE innovation. Yes, there will always be people who invent with no financial incentive (particularly for things that don't require any expense). However, there are millions of other people who are capable of inventing, but need to make a living. The purpose of patents is to urge THEM to invent. Whether that prodding comes in the form of making and selling your own products, or whether it comes in the form of a paycheck from someone else who is hoping to cash in on your work does not matter. The end result is things get invented.
And your example sucks. You did not invent anything, you just recreated something by using the knowledge gained from the people who did invent those things. Come back to us when you have actually invented a useful or desirable thing, and someone else is making and selling it cheaper than you because they didn't have to go to the expense of inventing it.