There has never been copyright for design. Copyright for source code and for binaries works quite well for protecting software from wholesale copying, piracy notwithstanding. Software ideas are a dime a dozen. The real protection comes from the difficulty of the implementation, the pace of change, and the first mover advantage.
Copyright is provided for the expression of a work. So if I tell the story of a girl who wears a red cloak and visits her ailing grandmother who lives in a remote estate, only to find her grandmother has been eaten by an anthromorphized wolf. I run the risk of violating the copyright on the story of Little Red Riding Hood. Except that it was a folk tale before 1900 and yet even though its 'out of copyright' there is a pall over whether or not Google can show you their scanned copy from 1909 of the story illustrated by artists at the time.
My thesis is quite simple;
1) There must be a doctrine for protecting the origination and implementation of complex systems, whether their components are manufactured from solid materials or are simply algorithmic components.
You'll recall that software patents came to be when it was shown that implementation via software was indistinguishable from implementation in hardware for some classes of problem. Your "first mover' advantage is worthless if someone else controls all the distribution.
Further, not all software efforts are 'trivial' and while we see those stories all the time I don't believe you could make a similar argument for the implementation of assymetric cryptography as a 'trivial' software patent.
2) The current system is clearly flawed in many ways, but the concept is not.
3) Pushing otherwise technologically illiterate but 'wanting to help' policy makers toward the concept that all software is more like creating 'art' than it like creating 'machines.' Would have the un-intended side effect of having those policy makers moving the necessary protection doctrine to the only other set of laws we have which are copyright.
Copyright, being even more easily argued than software, has been completely corrupted by media 'barons' and their efforts around the world. Which is why the question of whether or not I could legally copy a book printed in 1900 about a story that was 'old' even then, is currently 'questionable' whereas building a steam engine and selling it for profit is not.
1) There can be no doctrine to protect ideas, because any sufficiently complex software system to be marketable also relies on so many different ideas that the cost of licensing patents to enter the market is prohibitive. See for example the mobile OS market, which is effectively inaccessible for new players right now unless they have a billion-dollar bankroll.
Your example of cryptography is a bad one, because those ideas are usually developed in educational environments, funded by tax dollars. For those rare classes of software where the idea really is non-obvious and takes a large time to develop, government can provide the necessary funding to develop it, without the other 98% of software having to suffer under a restrictive patent system.
2) The current system is flawed conceptually, we don't need a software patent system, never did. It's a myth, and there's no cost/benefit analysis that ever proved it as anything else. We don't need a patent system for many other classes of invention also. In most industries it's a net negative, not much more than a tax on doing business.
3) Whether or not software is like making art has nothing to do with the legal situation. If the laws covering art are even worse than the laws covering technological invention then those laws need to change as well. That copyright has been misappropriated to the degree that it has is not something you solve by making less subject matter copyrightable, but by fixing the law.