Halcro. You are right, it's not necessarily a deal breaker. That said there is really no doubt in my mind that fewer connections are better, but often there are reasons it is not practical. It's usually not a night and day difference in most cases, and it can be swamped by other factors.
For the sake of argument, if integrated amps were built to the same standard as separates, and used outboard, separate power supplies for each section, then they could be better. There are a few reasons (at least) no one builds integrated's that way. First, they would have to charge an enormous amount of money for them. Second it is rare that any one manufacture is skilled enough to get the most out of every different section (phono stage, dac, line stage, amplifier). Therefore something in the design will be less than optimal. And third, allot of audiophiles like to have the flexibility to try different things without replacing the entire system.
For the sake of argument, if integrated amps were built to the same standard as separates, and used outboard, separate power supplies for each section, then they could be better. There are a few reasons (at least) no one builds integrated's that way. First, they would have to charge an enormous amount of money for them. Second it is rare that any one manufacture is skilled enough to get the most out of every different section (phono stage, dac, line stage, amplifier). Therefore something in the design will be less than optimal. And third, allot of audiophiles like to have the flexibility to try different things without replacing the entire system.