Selecting office holders in a similar manner to how jury pools are picked from the general population would lead to having leaders who are on average of average intelligence. As much as our current system is dysfunctional, and we like to call most politicians morons, the vast majority of them, with some notable exceptions, are of above average intelligence. But our system also selects for lots of negative traits like sociopathy that would be represented at a much lower level if offices were filled at random. It would be an interesting trade-off to see how it turned out. Probably would work better with political structures like Congress or a state legislature with many members so the standard deviation of personality attributes would overall tend to be dampened. For something like the mayor of a city, you're one bad random selection away from disaster.
In regard to your mother, I believe we erred greatly in giving unnatural persons like corporations most of the same rights as natural persons. I'd favor a system where only those who are eligible to vote for a particular candidate could advocate on their behalf, in any form other than casual personal conversation. Same would go for lobbying politicians once they're in office. Only those the office holder represents would have to right to lobby them and it could only be in a personal capacity. Office holders would be free to reach out to whoever they wanted, but without the quid pro quo of campaign donations, the nature of those discussions would be very different. Under those circumstances, she'd probably be a much better officer holder than many of the creeps we have running things now.