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A proportion of government spending is associated with welfare. There are also many factors related to poverty that may result in higher government spending (e.g. poor health, crime, etc.).
Does it follow that a society with a more even distribution of wealth would likely require less government spending and hence lower taxation?
EDIT: The research I found looks at income inequality, not wealth as the question asks.
Specifically with respect to social welfare spending (not necesserily taxation), the following articles from 2003 seem to suggest the opposite is true.
The political economy literature suggests that redistributive spending is higher in unequal societies due to median voter preferences. Alternatively, it can be argued that unequal societies may spend less on redistribution because of capital market imperfections. Based on different data sources, the cross-country evidence reported in this paper suggests that more unequal societies do spend less on redistribution.
The empirical relationship between inequality and social-insurance spending as a share of GDP in advanced industrial societies differs across policies. For many policies--pensions, health care, family benefits, poverty alleviation--spending is largely uncorrelated with the inequality of wages and salaries. But for a significant set of policies that constitute roughly 30 percent of the welfare benefit--unemployment insurance, active labor-market policies, sickness pay, disability insurance, and occupational illness and injury--spending is significantly more generous in countries with a relatively egalitarian pretax distribution of wages and salaries.
But your question is framed somewhat more broadly. Inequality may potentially lead to greater spending in other areas like healthcare, police, and so on. I'm not seeing any really comprehensive studies that try to take account of all that. In terms of deficits, Larch (2010) finds that "a more unequal distribution of income can weigh on a country's fiscal performance." This does not necessarily show that net taxes are lower in more unequal societies, but Larch does hypothesize that "an increase in the inequality of income tends to soften the relative preference for fiscal discipline". So I would say to answer your broader question, more research may be needed.
Typically in economics, government policy is considered as the independent variable -- that is, it's a thing that we can control and change, which then affects dependent variables, things like inequality. Asking if inequality affects tax rates, then, is a bit like asking if weather causes the sun to shine. The causality runs in the other direction. Tax rates are set by an act of Congress, not by the economy, and as a result the question of what makes congressmen vote for or against a bill to raise or lower taxes would traditionally fall under political science, not economics.
The other thing is that poverty is usually thought of as an issue of income, the amount of money a person can spend, not wealth. A person can have a negative wealth, because they have a lot of debt, and still be living a very good lifestyle, because they're making a lot of money and spending it. A surgeon who just got out of medical school would fit the bill here. The opposite direction is much rarer but could happen for e.g. a retiree who is living in a house that would be worth a lot if they sold it but who doesn't have much money on hand. As a result changes in wealth per se aren't connected to the issues you're talking about. However, changes in wealth and changes in income tend to go hand in hand. People making a lot of money will tend to save some of it and end up with more wealth, and people with lots of wealth can save it to earn interest.
