If Bishops were paid, they could devote their time to being a full-time Bishop.
I have a friend who said the above a few years ago, while we were talking about the stipends for full-time service at higher levels in the LDS Church. This post is a brief response to his statement - not full and complete, but enough to provide a decent outline of my feelings about this issue.
Personally, I don't want full-time Bishops working in that position as a career - and it would have to be as a career, since it would be cruel to ask someone to quit a job, work for 5 years or so as a Bishop, and then make them try to return to the work they did when they quit to become a Bishop. (Their service wouldn't be valued by most employers outside the Inter-Mountain West Mormon corridor, and it actually would hurt their employment opportunities in some geographic areas.) I don't want career ministers, even though there are some wonderful benefits in lots of cases. Part of my reason is philosophical, but part of it is practical.
First, I oppose making people get college degrees to qualify as ministers, and there would have to be some way to "qualify" Bishops and Stake Presidents if they were paid as full-time employees. The debt alone it wrong, in my opinion, for the purpose - as is the elitism I have viewed in many situations, including while taking a few classes at the Harvard Divinity School.
Second, I've seen too many examples of abuse, conceit, extravagance, etc. in congregations of non-Mormon friends to want it happening in the LDS Church (when the leader feels unaccountable to the membership), and I also have seen wholesale abandonment of doctrine in other cases (where the leader feels beholden to preach only what the majority of the membership - or even only a few highly influential members and families - want to hear).
Third, if we decided to pay our Bishops and Stake Presidents, what about their counselors - and the Relief Society Presidents, Elders Quorum Presidents, High Priests Group Leaders, Ward Mission Leaders, Young Women and Men Presidents, High Council, etc? Some of them put in almost as much time as Stake Presidents and Bishops, especially the ones who are retired. How do we determine who gets paid and how much they receive?
Fourth, paying local leaders would lead inevitably, I believe, to larger and larger congregations, in order to reduce payroll expenses - and I am not a fan at all of a mega-church model.
(If we ever decide to pay local leaders, I would favor a small stipend - perhaps the equivalent of minimum wage for 10-20 hours/week, although I haven't thought through that. Seriously, I haven't thought about it in depth, so take it with a huge grain of salt.)
Finally, I can hear critics (inside and outside the Church) wailing about how that money should have been spent helping the poor and for humanitarian aid - and I think it would be a legitimate discussion, at least.