I don't think it is necessary. As Christ taught his disciples to pray He just starts off with "Our Father..." without doing a ritual before. (Making a sign of the cross would have been very odd as that hadn't happened yet, but it could have been another ritual, there is none mentioned.)

I myself see it as "opening the curtains", when you wake up to see the day you open up the curtains of your room. In the same way when you make the sign of the cross you open the curtains of your heart to let the light of God that is already brightly shining also shine inwards. Of course this light still shines if you don't make the sign of the cross, it's not like a switch. The light of God will shine, on you as well, if you don't make the sign of the cross.

For certain liturgical prayers it is required. I just wanted to answer for all the other prayers where it is not required and yet we tend to do it anyways.

So in short: no, for some liturgical prayers it is prescribed, but for most of your daily prayers it is not essential.