LaFra
Yes, that response report cannot be customized. In our case since we had no compulsion of attaching we used a table in the email and made the response report with piped text.
Hope it helps!

Thank you Deepak, it's what I'm building now but the survey is quite complex so building with piped text it's not easy.
I see that the pdf report you can download from the Data&Analysis section is aesthetically much better so I wonder why qualtrics desn't use that.. Still investigating

LaFra
The one in data & analysis shows you the questions which were not shown to the respondent as well. But response report only covers the ones which are answered hence its more customized per respondent. Hence, it's the way it is.
Hope it helps!

According to the support page, you can have engineering create custom reports :
Qtip: By default, all answers to all questions and all embedded data are included in a response report. However, our Engineering Services team can create custom response reports to fit your organization’s needs. Contact your Account Executive if you’re interested in this solution.
For a more manual solution, consider using piped text in an email task. This will require building reports from scratch, which will not have the PDF export or live link.

Thank you vgayraud, I'll try working using piped text in an email task but I already know that it won't be the perfect solution.
Will contact my Account Executive to see if a more "design-ish" result can be achieved.