Unfortunately your competitors don't need your skills to copy you; once you make your thing public, everybody will see how to do it and copying your product becomes trivial. But the good part is that only successful projects are copied, so you really shouldn't worry about it -- when people start copying you, it means you are on the right track.
People copy when they know it's worth the risk. That's why successful projects are copied. I agree with you that it is a very good indicator that you are on the right track. :)
Of course, now that Twitter is established, you cannot repeat their mistakes if you want to succeed.
[1]http://highscalability.com/blog/2013/7/8/the-architecture-tw...
You'd think that Twitter with all their resources could have copied Instagram in a snap. Instead, when he saw the product and the traction, the founder of Twitter invested in it. He then got upset when Facebook brought them and is only now copying them.
There's more to a business than the code of its products.
All this design work isn't necessary when you copy something. Someone else has already done the design work for you. You can lean back and say: "The solution is obvious." Then you only need to implement it. In my experience, the implementation always seems trivial in comparison to the design process.
But you are right, people who copy stuff often make poor copies. I think the problem is that they probably don't fully understand your design. They see how you solved something, but they don't understand why you solved it that way.
Finally, I don't think a rebuild is the same as a copy, because you generally only rebuild when something doesn't work. And then you actually need to put a lot of design work into the rebuild process -- that's why it's hard.
Most developers I know find that the most difficult part of product development is sales. Design is also difficult but I'd recommend treating it as a process rather than a project when it comes to new products in new businesses. Design will never be done and it can always be improved, copycats will always be two steps behind or they'll fork into a different direction.
I know of financially successful products where the teams behind them don't know why the design they have works. They've even had situations where they've improved the design in their view and it's been well received in user testing. But when they release it, it has a negative impact on sales, retention or some other core metric. Imagine trying to copy a counter intuitive system like that?
If you have something where the core value is obvious and can be copied with ease you've probably released too late. Even in that case it would be pretty impressive if your marketing was so good that it found someone who could copy it. After removing the design part there are still very few people in the world with the time and resources to focus on building a copy right now. I'd guess that most people who think about copying will more likely become very good customers of yours, they can then have more time to work on their own ideas.
Or products that are so brilliant that it's immediately apparent they'll be successful