I posted a message that matches your request. the link: https://discuss.tryton.org/t/how-to-manage-the-name-of-generic-products/
The idea is not to add an additional field but to display the summary (first line) in the list views. This not the addition of a function field.
However, I agree with you about the problem of having the description of the invoice line in a different tab. This requires changing tabs at each encoding for a line. I will propose a modification to move the field and see the opinions of others.