Depends on what you mean by "poor" especially "to poor to pay taxes." In the US, a family of four has to be making over 50,000 per year before they start pulling their own weight. The tax burden follows Praeto's rule, 20% of the population pays 80% of the taxes. If not being a tax burden is your definition of poor, then even in developed countries, half or more of the population is "poor."
Prior to the Corporate/Industrial age. The agricultural poor paid the majority of the taxes while the nobility paid nothing. France had a little to-due about the imbalance circ 1782.
The tax burden didn't fall off the poor until corporations really got going generating more wealth than agriculture and in a more concentrated and seizable area that a butch subsistence farmer scattered all over the country. (Famously, the Dutch East India Company was created when the government of Holland forced many small companies into one in order to protect the states tax revenues that paid for their war of independence.)
The poor in the 3rd world are much different than the poor in the developed world. The 3rd world has corrupt legal systems, no protection for private property, and therefore few corporations which apart from being revenue sources are also necessary for the building and running of modern technological assets. As a result, the poor are one way or another a major source of tax revenue and their labor desperately needed in a virtually pre-industrial economy.
Subsistence farms absolutely require the physical labor of children to by. Price fixing for the urban poor, keeps rural farmers poor which in turn means they must rely on their own children for labor, hence higher population growth than necessary.
Therefore, unless you have a first world economy, the state will need a lot of poor people for its own survival.
In the developed world, we don't don't have people who are materially poor. The average poor person in the U.S. today, has a material standard of living equivalent to that of a middle-class person 50 years ago and the material conditions continue to improve. The millions who flock to the US every year to work hard and off the books just to be poor is good evidence of this.
"Poverty" in the developed world is viewed both historically and compared to the 3rd world, much more like calling the least wealthy guy at the country club "poor". We're the first civilization in history to have obesity be a health issue for the poor, because food is so cheap and labor so light.
Jesus said, "The poor you will always have with you," and he was right because it’s a condition relative to condition of others in society. The goal post are constantly moving. No matter how much better off those who have the least in a society may become in absolute terms, as long as everyone else's lives are also improving at the same time, somebody is still relatively poor to someone else.
The real sting of poverty in the developed world is not material want, but the pain caused by the perception of the poor that they are off low social status. Human's evolved with virtually no material safety and our brains tell us that high status and dominance will make us happy. Even if you did manage to somehow humanely decrease the percentage of people to unproductive to pay taxes. Those who now found themselves at the bottom, no matter how materially comfortable, would now feel "poor" and the cycle would start all over again.