IMO, there needs to be a recognition of all factors in order to determine the justness of a behavior or transaction, and surely all of us agree that a government's job is to enforce justice (even if we disagree on what that definition is). It appears you're basically viewing "consent" between two people as the be-all-end-all, without recognizing some relative power structures that go in to offering that ostensible consent.
For example, surely we recognize that survival and desperation are some pretty key factors. Taken to another extreme, imagine a situation where a woman is starving, someone comes up to her and offers a Big Mac if she'll sleep with him (but only if she agrees to waive any and all paternity claims that may arise from this liaison), and she accepts. Because, you know, starving. There's been offer-acceptance and "consent", but due to the the desperation that woman is facing few would argue such a transaction is "just", you could even argue that she didn't even really "consent" as a result of that desperation. I think few outside of the hardcore libertarians would argue such a transaction would be permissible in society. We therefore have laws that prevent said transactions from taking place, regardless of the "consent" that either party might offer. For a less offensive example, imagine something like blackmail which could be considered a "consenting" transaction but we still don't permit that or recognize said offers as valid due to that (as well as the negative social impact those transactions have). Safety regulations ("you agreed to work in that mine that you knew could collapse"), we can go on and on with plenty of examples where
You're right, there's a subjectivity to all of this. Governments are comprised of people, and prone to corruption. Populism can cause inefficient decisions. That shouldn't be disputed. All of that needs to be factored in when discussing whether something is "just" or "fair". I just don't think you can view it is as some black and white objective claim that boils down solely to consent, when the factors that determine consent can vary wildly.
That would probably depend on whether the increase to necessarily decreases the opportunity to work. If we increase the Min Wage to $100 / hr, we would agree it almost assuredly would. Whether more modest increases to the min hourly wage substantially reduce that opportunity is less certain. Very complex topic.