When Picard mentioned that having 4 shifts would be too expensive, personnel-wise, Jellico could have made a comment about thousands of cadets graduating Starfleet Academy, and half of them wanting to be on board Enterprise. Picard could have been given a list of the top 10% of the graduating cadets, several promising ensigns and lieutenants, and selected 200-300 to fill out an additional duty shift. One request taken care of, and everyone on board gets to have 6 hour work days, instead of 8 hour work days (or more time for weekends/days off).
Basically Picard could have been given all the personnel he needed to make up a 4th shift, he just didn't want to because it was different.
As to the Away Team, there should have been a bunch of specialists, with dedicated Medics. At most Picard might have gone, and even though the specialists would have been annoying and portrayed as too militaristic, their motto of "First in, last out", means that they volunteer to be redshirts. One of them would be forced to leave Picard behind, and his last workds of "I'll come back" would be right as he is transported out. Once they go back for Picard, that one is so loaded down with gear that he cannot move too far, and is a potential explosion hazard from the charged power packs.
Hmm, fun with numbers (aka really long tangent below):
Assuming Starfleet is similar to the
US Navy, then there is over 3:1 ratio of actual Starfleet officers to Academy midshipment (including those still in the Academy and those underway and undergoing evaluation).
Here is the relevant information:
Officers: 52,715
Enlisted: 276,413
Midshipmen: 3,351
This is roughly 15.7:1 ratio of officers to deployed midshipmen (aka not including the ones still in school). I got bored and ran some numbers from the DIT main site, comparing number of ships built with the number of officers assigned to them. That gave me ~1.67 million personnel on Starfleet ships. With the 15.7:1 ratio, that means there are ~100,000 midshipmen in Starfleet.
Heck of a school, graduating ~100,000 beings a year, or ~8300 per month, or about 273 per day. Assuming Starfleet lasts for 4 years, that is a minimum of 400,000 beings attending school (not including dropouts every year). In UK terms, that is roughly between the Leicester and Bournemouth Urban areas in terms of population.
From
Menage a Troi, we are told that Wesley missed going to the Academy for one year, but can apply for next year. This means that once a year there is a flood of new arrivals at Starfleet Academy.
Now if you assume that 4 arrive on Earth, but only one is accepted (from
Coming of Age), then once a year, there are suddenly 400,000 additional people arriving, of which 300,000 will be sent home. So for brief periods, Starfleet Academy is the host of 700,000 people (3 existing classes of 300,000, and 400,000 hopefuls). Must be a heck of a party town when that happens, not to mention the depression afterwards. Transport ships probably hang around for the rides to/from.
Of course, this is an upper limit, as several of the ships I used for my numbers have been decomissioned and no longer count, but it does put us in a rough ballpark for Starfleet's strength.
