There's no reason to do that. You do not want to create more methane, and the possibility of even a trickling of it getting into the atmosphere. This methane to methanol is purely to get rid of the methane we produce, and hopefully the methane stored in the atmosphere. We've got plenty of hydrogen, it's one of the most common elements (iirc) in the known universe, but to convert some into methane? Hydrogen is clean, and then make it toxic methane? It's much better to just use the hydrogen as fuel. I remember seeing an article one time about a method to convert hydrogen into fuel, and so it's much better to do it that way. Though how costly or doable on a mass scale either conversion is, we don't know yet.

I don't think you need to go through methane to get from hydrogen to methanol, you just synthesize methanol directly once you have the hydrogen. In fact, most methanol is made by splitting hydrogen from natural gas first.

This is more useful for producing methanol from biogas (i.e. waste facilities), since the gas is produced by bacteria as part of the natural decay process. It's an alternative to producing methane catalytically from hydrogen.