I think it is not necessary to pay for software to have "contract" and use a license. The license defines limitations and rights to do a copy or copies (redistribute). When you install the software, you make a copy and have to accept the license. Before you make any copy of software, the license is like offer - describes the conditions. About EULA, I am not a lawyer and not sure but I think there is difference between copyright violation and breach of agreement. Probably with the agreement is easier to start a lawsuit.
Yes, perhaps, but what I'm getting at is this:
If you pay for a piece of software, you technically enter into a contract, providing all conditions of entering a contract are present. If you don't you may be implicitly in a contract but it's basically unenforceable. Either way, for general software you and I use, it's not a contract as your country's contract law would define. It's more of an "obligation" than a contract. It is more enforceable when money changes hands because there's an incentive to seek compensation though the courts.
If I enter an agreement to purchase a 1000 copies of Windows 10 (eek!) for my business, I sign a contract with M$ that I will pay them. The EULA is secondary "protection" for M$ for all those who do not sign a contract with M$, like the average user who gets it with their laptop or works at my business.
Look at all the EULAs around. Most EULAs I have glanced through are full of attempts to protect the issuer. They don't mention anything about contracts, because they aren't. Contracts (in most jurisdictions) have a test of capacity: you must be able to understand what you're signing, not be mentally impaired, not be a minor and so on. None of these conditions exist. A lot of EULAs breach consumer laws because they attempt to reduce your rights. Most have never been tested in court.
That's why a software license, a là EULAs, are mainly unenforceable and rely on pressure from their creators, like Microsoft, Adobe, Apple et al to influence governments to protect them via copyright protection and enforcement. They don't want to do any of the enforcement because it's basically impossible. Try enforcing a "contract" with a 12 year old minor who bought a laptop with M$ Windows installed. It's much easier to use copyright law because it's got a much vaguer set of rules for what "infringement" means.
Anyway, when all is said and done, that's why permissive licenses are superior. They're not viral like GPLv1-1000 and by-and-large their only requirement is keeping of the license message in the software.
(Wow this got sort-of off-topic-sort-of).