The question was asked: if repairs can be done from within the ship why would a workpod be needed?
What if the ship sustains physical damage that cannot be accessed from inside?
I’m also wondering about the shuttlecraft numbering system. In The Making Of Star Trek it’s referenced the Enterprise has seven shuttlecraft, and we interpret that as seven Class F shuttlecraft. This does line up with he Galileo being registered NCC-1701/7. But over the years it looks highly unlikely the ship carries seven such vehicles aboard as there isn’t enough room. They must have realized this back in the day because in “The Omega Glory” they establish a Constitution-class ship has four shuttlecraft. That seems much more reasonable given the space available aboard a 947ft. ship.
But now having Galileo registered as NCC-170/7 rather 1-4 doesn’t line up anymore.
In TOS we only know the Galileo’s registry. Although we hear the Columbus mentioned we never see its registry because they just reused footage of the Galileo. Much later in TFF we see the Copernicus (sporting a new design) and its registry is 5, and this could or has been retconned into TOS, but that doesn’t count here just as whatever TOS-R showed doesn’t count either.
Unfortunately, to the best of my knowledge, no list was ever drawn up of possible shuttlecraft names. “The Galileo Seven” is the only time names of shuttlecraft were ever referenced. After that they were just referenced as shuttlecraft.
In my own drawings when working up plans for the Class F I eventually opted for Galileo, Columbus, Copernicus and Magellan—two astronomers and two explorers. Mind you thats not set in stone, but just what I thought reasonable.
But even so why a registry of 7 when there are supposed to be only four shuttlecraft as complement? Possibly in Season 1 they still thought it was possible to berth seven shuttlecraft aboard, but more likely they chose 7 because it was easier when making up the markings for the vehicle because you just needed an extra 7 from 1701. Pretty much like what they did later for the Constellation and its registry 1017 being a rearranging of 1701.
One explanation could be that as shuttlecraft were lost over the years the replacements were numbered sequentially higher. So the Galileo could be the seventh shuttlecraft the Enterprise has had since it launched. The problem with that explanation is later the Galileo II is also registered 1701/7 rather than 1701/8. So while reasonable it doesn’t work based on what we see.
But what if the Enterprise has other smaller auxiliary craft to make up a total of seven small craft aboard ship? So four shuttlecraft and three workpods?