Do rich parents pay less in child support if they didn't provide a
rich lifestyle for their family pre-divorce?
Yes and no.
There is a standard schedule of presumptive child support payments based mostly on the gross income of each parent in every U.S. state. This schedule is largely the product of requirements imposed for state eligibility for joint state-federal welfare programs. But this schedule tops out at roughly upper middle class incomes with the top of the scheduled roughly providing a presumptive floor for the children of higher earning parents. Depending on the state, perhaps 1-5% of divorcing couples with children are above the schedule.
Above the schedule, child support is far more discretionary.
Effectively, the default rule is to extend the schedule up proportionately to higher incomes, but the higher the couple's incomes, the less relevant the schedule amounts become. No court awards the same percentage of income to children in a family where there is $1 billion of income in a year as it does in a family where there is $100,000 of income in year.
Above the schedule, the standard of living maintained for the children prior to the establishment of a child support order is an important factor in establishing it. But there is no firm formula or schedule to determine it. No one factor is controlling.
It is also worth noting that the lifestyle in which the children have been raised alone isn't determinative of the relevant lifestyle for a court to consider. Courts are going to be generous towards children who have been raised as if they were of very modest means, while the parents themselves live an extravagant lifestyle.
Essentially, what courts try to do is reproduce the economic support that the children would receive if their parents' relationship was healthy and the parents treated their children reasonably and equitably.
Normally Alice would be forced to pay a lot of money ($20k/month?) to
Bob in child support payments due to her income, with the argument
being that the divorce shouldn't disrupt the childs lifestyle.
Part of the issue is that above a certain income level there is no "normally", there are only lots of particularized exceptions.
Roughly speaking, the schedule works out to about 12.5% of the combined income, prorated by relative incomes and the percentage of time spent with each parent, per child. But as one gets far above the schedule, this percentage becomes largely irrelevant and the right answer gets very fuzzy and depends a lot on the individual judge making the decision and upon the presentation made by each parent's lawyer.
And, keep in mind, that even when the parents' combined incomes are very high, probably 90%+ of cases will settle. So most of the time, the judge won't rule at all on the question, and the "shadow" of how the judge might have ruled in these cases is very faint.
Few cases are decided by judges each year at this level, nationwide. Fewer still produce appellate case law to guide judges in similar cases in the future, in part, because the case law affords judges immense discretion in these cases.
Indeed, some of the really eye popping child support rulings involving a wealthy parent or parents are de facto court sanctions directed at an obstinate wealthy parent whose lawyers overplayed their hand and left a disgusted judge feeling that this parent wants to treat his or her children like Cinderella, when the children deserve better and the wealthy parent can easily afford to pay more. If a wealthy parent is too aggressive it starts to make the judge feel like the parent isn't taking the court seriously, and it makes the judge feel like the wealthy parent isn't litigating in good faith.
Divorce cases are decided by judges sitting in equity, and in equity cases, the litigant who seems to the judge to be acting most reasonably usually wins. When one parent takes very unreasonable stances, the other parent can ask for a lot and still win that battle.