ELI5: Why didn't modern armies employ substantial numbers of snipers to cover infantry charges?

I understand training an expert - or competent - sniper is not an easy thing to do, especially in large scale conflicts, however, we often see in media long charges of infantry against opposing infantry.

What prevented say, the US army in Vietnam or the British army forces in France from using an overwhelming sniper force, say 30-50 snipers who could take out opposing firepower but also utilised to protect their infantry as they went 'over the top'.

I admit I've seen a lot of war films and I know there is a good bunch of reasons for this, but let's hear them.