That is how I worked my first season - a 21" Toro on a cargo carrier and the rest of my equipment in the bed.
Last year I bought a 36" Ferris hydro so I could take on some larger properties.
I have "city days" where I only use the 21" - there is no other option - no other mower can be used due to either lack of access, or terrain. Mixed in with those jobs are a few that I COULD use the 36" on, but overall, it's not worth the hassle of dragging a trailer around and trying to find a place to park it.
Eventually, I'll be able to transition away from the smaller lawns and, add a ZTR and take on more profitible jobs, but for right now, I do what I can with what I have. I can tell you that there are plenty of people who work in the city using nothing more than a 21" mower, so it can be done if you use your head, and get yourself a nice clientel list.
Also, in regards to the comment made by the OP regarding the look of hauling a trailer with nothing but a 36" - "Who cares?"
Do what works for YOU. People (mostly anonymous internet landscapers) will make fun of my setup. When what they think starts paying my bills, I may begin to take note, but until then, I do what works best for me.