I think you could pretty reasonably get by without a towed vehicle on the trip, but also there probably are times where you could make good use of one if you had it. Its presence or absence might tend to alter what you end up doing--and it sounds like a fabulous trip in any case.
I find that, for me, there's little reason to bring a towed vehicle. I do sometimes carry a bicycle, and sometimes have to get a little exercise walking from where I can park or camp to where I want to be. I also at times make use of public transit. That said, parking at places that are outside of large cities is not usually a big problem, particularly if you're willing to park at a slightly remote spot, and stopping for groceries or other supplies en route is not at all tricky to manage when you're moving from one destination to another every few days or oftener. Camping at one location (particularly one not served by other transit) for a week or two or three is somewhat of a different matter.
That said, there's no doubt that there are occasional limitations to not having a towed car, and I'm sure I choose trips and destinations where it's not a problem while I may do otherwise if I travelled with one. Similarly, there are probably a few places I've gone or things I've done or places I've gotten fuel that I would avoid if I had a car towed behind. There are also a few trips I've made in a car that I would be less likely to do with the motorhome.