Op, keep in mind that European universities are not holistic - if you have the stats, you’re more or less in. For Bocconi, there is a motivation letter, but a basic one (by US standards) is fine - talking about how Bocconi’s international reputation dovetails with the student’s international background and goals is sufficient as far as “why Bocconi” goes. They also aren’t going to reject an international student for signaling wealth - there is a reason why internationals pay extra.
The personal statement is important for LSE, but it should be centered around “why economics” and your supercurriculars in that econ/math rather than why LSE (your personal statement goes to all the UCAS universities you apply to, so it’s considered presumptuous to mention one by name)
Also, neither Bocconi nor LSE do interviews.