It doesn't strike me that 'Mill seems to be stating that [pain] is a necessary component to happiness'.
Like many moral philosophers Mill doesn't have in mind an ideal world. As sentient beings, humankind is (on the whole and rare exceptions aside) vulnerable to pain. The human predicament can be improved in several respects but susceptibility to pain ...
what happiness is supposed to be and how it could be measured (to maximize it)
We can't measure it directly so we use voting instead in democracies
what the target group should be (whose overall amount of happiness is to be maximezed)
The group is the total number of people impacted by the action you're considering
But maybe this still isn't the whole ...
With utilitarianism actions are always judged based on the consequences.
What if the consequence can't be evaluated ? Then you have a high risk of doing something wrong.
You have to remember that utilitarianism is recursive. Therefore you have to act so that your choice has better chances of being the good one, therefore you have to study your options.
I don't know why you are trying to put equations on something so blurry. If equality is good then it's good because, and in as much as, it promotes happiness. There you go, I reconciled the 2 theories.
But I doubt you could reasonably value the happiness contribution of equality in numbers. And for many reasons, the communists tried and failed.
The thing ...
This question applies to humans as well. With utilitarianism you have to consider an infinity of factors, however if we consider the individuals as strictly equal in all things, then yes there is a balance between improving a little for many and improving a lot for a few.
Nothing in philosophy is self-evident (except some areas of logic), but professional philosophers generally agree that acting according to "strong" utilitarianism requires altruism.
To use Sidgwick's language, strong utilitarianism demands that you adopt the "the point of view of the universe". In other words, when you act to increase utility, you must be ...