But the new item won't have the enhancement of the other. There's a reason why some abilities come with pluses and some not.
Yes, that's why it's something the Pact of the Blade Warlock would spend an invocation on. You have to get some benefit out of the invocation, or why have it at all?
The question is whether or not the benefit is ridiculously overpowered, or something in line with what you would expect from a class feature that revolves around summoning a magical weapon granted by your Patron.