It totally depends on the company.
Most "on-call" work isn't really "work"; you just get the beeper that the shift workers will page when there's a problem requiring a solution more technical than "reboot the machine and see if that fixes it".
If this "on-call" position actually requires you to be on-premises during the on-call time, whether there's a problem or not, then you should be paid for it; it's time away from your wife and kids. If the "on-call" work de facto requires you to be in the office all night, there's a serious problem with your infrastructure and you should spend daylight hours working to fix the problems that are keeping you up on your on-call nights.
At my company, there are a few individuals in various departments who are the "go-tos", day or night, for problems of various types (technical, interpersonal, business, etc). They are recognized by management and compensated for their expertise and work ethic accordingly, even though our business and its systems are, for the most part, pretty well-oiled and don't require a lot of technical intervention.
Sounds like your boss may be trying to do an end-run around having to recognize anyone in particular for extra effort by spreading it out among the technical staff; if everyone has to do it, it's nothing special so nobody gets kudos for it. Understand that if this is the motive, the move, from a managerial perspective, is a stroke of genius; If on-call work is really a serious commitment worthy of more pay, then you're not doing the job properly during your daylight hours. If you are the only one coming to the boss asking for more money because of this new on-call rotation, then you stick out; everyone else is taking it in stride, so your concerns look minor. And even if the entire technical staff comes into the boss's office at once voicing concerns, someone's gotta be on call; this is the "fair and equitable" method. If everyone wants more money, it's harder to fire all of you or stand by while you all quit if he can't or won't agree, though I would be extremely surprised if that happened over just this one thing; your job would have to be a pretty serious hellhole long before this came up.