Also, welfare is based on taxes. A tax which helps one person forces another into poverty, and it encourages people to be tax evaders. This is not good. Each little tax adds to all the other little taxes to make a burden which hurts everyone. The claim for free legal services is different in different contexts.
Some legal interests are different from others.
When people seek something such as a dissolution, it is a benefit, or a change of status, which is no different from any other benefit, and so the case saying a party has a right to a free divorce filing fee, which is a user fee, is wrong. This is quite different from being the party that another party is trying to take something money or liberty from. Judges are elected and the voting public cares about a fair verdict if there is a disparity between lawyers and unrepresented parties. Most judges do try to accommodate unrepresented parties, partly because they have to answer to the electorate. A person who goes to school will be better able to represent herself in court, so here again is the inducement to go to school and learn.