Citation needed; eliminating patents in general or software patents in particular would hurt some companies (notably patent trolls and other companies who make most of their money on patent licensing) and help others (notably those who regularly get sued by those companies, and those who spend time and money writing and filing patents and creating cross-licensing arrangements for defensive purposes).
The question of which of those will have a larger impact on the economy, and for that matter which behavior we would prefer to see encouraged, remains open and does not have a well-known or accepted answer as you've implied.
In your example, companies who get sued over patents today, would instead just see their products copied wholesale and sold for much lower prices, since the copying companies have no investment to recoup. Without the possibility of recouping investment, new product development would slow, stifling innovation across the economy. Which in turn would harm companies that exist solely to copy other products, since there would be fewer new products to copy.
> In your example, companies who get sued over patents today, would instead just see their products copied wholesale and sold for much lower prices
I think you mean "companies who sue over patents", not "companies who get sued over patents"; the latter are not the ones looking to prevent copying.
I'd also point out that that issue doesn't apply to software patents, since copyright already handles that issue quite effectively for software.
> Without the possibility of recouping investment, new product development would slow
Standard patent rhetoric. The corresponding anti-patent rhetoric would be that without the issue of spurious patent lawsuits and workarounds, product development would accelerate. Both claims require evidence, not just assertion.
> Which in turn would harm companies that exist solely to copy other products
Because of course the world is divided solely into companies that love patents and companies that exist solely to copy other products.
There's a large ecosystem of innovative companies that treat patents as overhead and cost rather than value.
The question of which of those will have a larger impact on the economy, and for that matter which behavior we would prefer to see encouraged, remains open and does not have a well-known or accepted answer as you've implied.