It is interesting to see the differences in elections between units, but in the end, each unit needs to figure out the structure that works for them.
My son's troop, has elections, generally in May with terms that take effect generally in September. The elect every position, although not every position is used. For example, sometimes there is a bugler, or historian, etc, sometime not. They even have the entire troop elect the patrol leaders. Admittedly, the patrol method vs. troop method is lacking in this unit, and something the new SM is trying to build up. Even the Den Chief position (if someone wants one) appears to go through the election process. After the elections, the SM may appoint some unelected (or discouraged from running) older scouts as troop guides, etc.
In general, I'm not a fan of much of this methodology. I find the leadership for most functions (as observed from a visitor to the Troop meetings and occasional campout) lacking and disorganized. The SPL does not always get along well with some of the other leadership staff, and so there is a serious lack of integrated effort. This is for a Troop of about 20+/- boys, organized into two or three patrols, 3/4 are 13 or under. This unit has more parent/leader coordination on activities and events then I would like to see, but the unit may not have reached a critical age/mass to be more boy run - I don't know.
The troop I grew up in, 50-60 boys, Fairly even age distribution in 11-16 range, some in 17 range. 7-8 patrols including the "leadership corps" organized as their own patrol; had elections every six months.
Week 1, Scouts wishing to run for SPL would announce themselves and describe their vision and qualifications to the troop.
Week 2, the Troop votes and the SPL is elected. The SPL then chose his own staff, which was typically 2 ASPLs (one in charge of the indoor program - troop meetings, one in charge of the outdoor program - campouts, etc.), The Scribe, The Troop Quarter Master, sometimes a historian or librarian, but not usually. If there were any JASMs, they were usually part of the leadership corps patrol (until we had to many of them, and they also became their own patrol). At the time, Troop guides were not used.
Following the staff selections, Scouts who wanted to transfer patrols (or outgoing/unreelected leaders) were moved into their new patrols. Week 3, The newly reorganized patrols then met and elected a Patrol leader, who in turn appointed is assistant patrol leader, the patrol scribe, and the patrol quartermaster. Sometimes after the patrol elections, some additional troop leader positions (i.e. the librarian or historian) might get staffed, but again, this was not common.
For this troop, this methods seem to work out well. While it is true, that some youth members may have had difficulties getting a PoR; in general SPLs quickly learned to choose people who could do the job over picking their friends; and the troop and patrols would make similar choices respectively. This was a very Boy run troop. 4-8 Adult leaders (also organized as their own patrol) were very behind the scenes. The boys made campsite reservations, each patrol was responsible for their own menus, did their own shopping, organized parent transportation, and maintaining patrol equipment (checked by the Troop QM), shifts on a paper recycling fund raiser. The adult leaders had a slightly bigger role in organizing Summer camp and an annual skiing trip, and in maintaining the canoes, canoe trailer, and a Santa/parade float we used for the Christmas season; but staffing the float was again on the patrols for each day they were assigned.
While I understand the concerns of those that like broader elections, I generally think just voting on the SPL/PLs tends to make a stronger troop, and tends to motivate the boys to do a good job in front of their peers so that they do get elected or chosen.