It seems to me that the SpaceX Starship rockets have sort of a homemade quality to them, like they were made in someone's garage with basic tools
That is because they are!
The "zeroth" prototype, Starhopper was built from November 2018 to March 2019 literally in a dirt field in Texas, in the open air. When Elon Musk announced in December 2018 that SpaceX was abandoning carbon fiber as the construction material and switching to stainless steel, he also announced that they had already been building a prototype test article for several weeks.
Despite the fact that they were building Starhopper out in the open, in a field, on the side of a public road, a lot of people did not even realize that what they were building there was a spaceship prototype. The mental disconnect between what they were seeing and what their mental image was of how "spaceship are supposed to be built" was just too big for them to comprehend. Spaceships are built in cleanrooms by people in white coats with facemarks and hairnets, not by a hired tank welders in a dirt field on the side of a road!
And yet, that is exactly what SpaceX did. Including the tank welder part: according to the logos on the side of their trucks, Starhopper was at least partially built by contractors who normally build water towers. (Which is where the "flying water tower" joke comes from and why it is so delightful that SpaceX actually did turn Starhopper into a water tower instead of scrapping it.)
In the beginning, there was only a dirt field and a tent for workers to store equipment and parts in:
Video by Austin Barnard
They didn't even have a windbreak or a way to secure the nosecone, which is why Starhopper flew without one: it was blown over and destroyed by the wind.
Over time, SpaceX added more tents, a windbreak, the midbay, and the highbay, they hired their own welders, they bought welding robots, they switched to a different alloy of stainless steel, they are developing their own alloy of stainless steel, and so on. So, each new prototype actually looks better than the last one.
But, in some sense, they are not even building Starship prototypes. One of Elon Musk's mottos is "Build the machine to build the machine", and that is what they are doing down there. You can almost think of it like the factory is the prototype, and the Starships are just a by-product. (Which is for example why they partially built SN 12–14 and then scrapped them again without ever testing them).