Virtually any tax benefit that has an income ceiling is off-limits to MFS taxpayers.
Many of my students wonder why MFS taxpayers can't get those tax benefits allowed to every other filing status.
Here's my answer: consider the case of Bill Gates' wife. Let's suppose she had only a small amount of income in her own name, because she spends most of her time on volunteer work. If the tax laws allowed a MFS filer to qualify for those tax benefits, taxpayers like her would be eligible to receive them, even though they are clearly not the intended audience.
However, IF our legally married taxpayer maintained a home for herself and a qualifying child AND if she did not live with her husband during the last six months of the tax year, she may qualify to be "considered as unmarried" for the purposes of Head of Household (HoH) filing status. In that case, the taxpayer would be eligible for all the low-income taxpayer benefits that would have been denied to her as an MFS taxpayer.
So, the only way that a married person like Melinda Gates could potentially qualify for HoH filing status would be to be live with one or more of her qualifying children in a separate household from Bill for more than the last six month of the tax year AND to have provided more than half the costs of the household herself.
MFS filing status is always a worse deal for the taxpayer than HoH filing status, so it is important to always work carefully through the filing status charts to consider the HoH possibility.
Some taxpayers have no alternative, unfortunately. Suppose, for example, a taxpayer lives by herself, but is legally married, even though she has no absolutely idea where her husband is. Or perhaps she does know where he is, but does not want anything to do with him, because she is a victim of domestic violence. Her only legal filing option might be MFS.
Of course, a legal divorce would solve the taxpayer's problem and allow her to file as Single, which is not as good as HoH but much better than MFS. However, divorce is often an expensive and difficult proposition for low-income taxpayers.