Tech people I know generally agree that patents and copyright stifle innovation.
Do you not know any "tech people" who are fond of the GPL? It relies on copyright to function. The same goes for enforcing the attribution requirement with Creative Commons.
There are a lot of things I would like to see changed in both copyright and patent law. I am a proponent of a "thin copyright" similar to that proposed by Siva Vaidyanathan, and I believe that software patents do not fit into the current system at all. I think eliminating the legal recognition of intellectual property entirely, however, would be throwing the baby out with the bathwater.
The fact that the GPL uses copyright is just an implementation detail.
In actual practice, it does the opposite of normal copyright. Copyright is usually used to restrict access to some work. A public domain work can be accessed to anyone, but, as it evolves, future contributors can restrict access to it. A GPL work remains accessible to everyone in perpetuity, not just from a legal standpoint but also from a practical standpoint (no need to reverse engineer or disassemble). Not only are you allowed to use the work, but also nobody is allowed to stop you from using it in any form. It really is on the opposite side of the spectrum from normal copyright (we can imagine public domain to be the midpoint).
In the FSF's perfect world, the GPL would not be necessary. Instead, you would be able to access and modify all your software without restriction. The GPL is just a clever way of creating and enforcing such a world without changing existing legislature.
Also, "intellectual property" is an unfortunate and rather loaded term. For one, it covers several distinct concepts like copyright, patents and trademarks which all behave differently and have different ramifications. Secondly, it presents a false parallel to real property. Whatever you think of Stallman's ideology, you have to admit he is a good writer (certainly infinitely better than I am) and very clear; here is his case against the term "intellectual property": http://www.gnu.org/philosophy/not-ipr.html
A final note: while the general software community is divided on patents and copyright, I don't think most people are against trademark law. If anything, trademark law is about fraud--you're not allowed to lie to customers about being affiliated with a known, existing brand. I suspect most people arguing for copyright and patent reform are fundamentally fine with trademark law as is, or want minor changes to it at most.
Normal copyright gives an author a "bundle of rights" that they may license how they want or declare to be in the public domain. Even if you classify the GPL as "copyleft, not copyright" or "legal judo," I don't think it works opposite of the way that normal copyright does. In a world where everything was public domain it would still be possible to circumvent GPL's source code distribution provisions.
There is one part of copyright that might run counter to the GPL, however, and that is the right of an author to reclaim copyright after 35 years. If the right applies (i.e. not a work legally classed as work for hire) it cannot be revoked, even by the author, until the 35 year term is nearly over. This right is generally a good thing, but might be a bit messy or disruptive if someone who wrote old UNIX IP decides to try to reclaim their work.
Unfortunate or not, intellectual property is a term of art at this point. However, connotation can differ from denotation, and it often does in law.
I'd prefer if for software, the only possibility was something similar to GPL v3+. Meaning: instead of copyright as it is known know, the law contains the terms of the GPL. So for any software you must be able to request the source code in a usable form.
Currently, copyright allows software to be released in a restricting (binary) form. As a result, the client always has to rely on the software vendor.
I rather have more competition in that. When software is created, I think there should still be a few possibilities. I think it is good if a company can still charge for software per copy (have to make money; support isn't everything). So for each software it should be possible to restricts its distribution (like copyright atm). However, a client should be able to hire another company and make their own modifications to that software (in some cases you just have to keep the changes to yourself).
At the moment any software basically results in a monopoly. Especially within bigger companies (loads of software which source might not be available anymore, etc).
GPL is often seen as communism. But IMO the current situation doesn't allow for much competition. Law should be always adjusted to ensure (healthy) competition can take place.
To be clear: I am not advocating that every software company should work like the current free software/open source software companies. Read by post again if you thought that.