I imagine there are a number of factors coming into play here:
The restaurant as we know it emerged in the wake of the French revolution, which means that being a waiter wouldn't really be a viable job option until the 19th century. In the 19th century, we also saw the rise of writing fiction being a viable means of support (which, sadly, is no longer the case and there are perhaps 250 writers of fiction in the world who make a living exclusively from writing fiction).
Being able to write was in itself a specific qualification for much of this time period. If you were sufficiently literate to be able to write, you were also sufficiently literate to be able to get a job which exploited your literacy, thus, e.g., Hawthorne working at the customs house, Trollope at the post office, etc.
Status likely plays a role as well. Actors (stereotypically working as waiters before their “break”) often came from the lower classes while writers much less so (although there are certainly exceptions). Many of the writers whose names have come down to us from the 19th and early 20th centuries came from middle or upper class background (although, again, not all) and thus might have been unwilling to take a job which they considered beneath them.
All this said, there are, of course, the exceptions to the above assertions. Dickens famously worked in a blacking factory when his father was put into debtors' prison, although he did later return to school and worked as a journalist before embarking on his literary career. Herman Melville also had an impecunious father, but he still worked a number of white collar jobs before his stint as a sailor which was the preface to his literary career.