The seat post idea is great. If you could adapt a monopod with a ball head to fit the seat tube, you could have some of both. In fact, you could strap or shock cord the center section of a tripod or a monopod to the outside of the seat tube. Some rubber tape or section of inner tube would keep it from slipping.
It's all about priorities. People who haul lots of camera gear have made quality image making a priority. I've always said there are two kinds of photographs: high quality purpose-driven images for art, journalism or commercial use and then "shots of record" that are note cards on people, places and events in our lives. The term snapshot is good, and implies simple gear and images made with little or no setup or manipulation.
So, if your priority is to make shots of record, then you should minimalize your gear, keeping it simple, light and ALWAYS AT HAND. I think this is where phones excel. Hi-res point and shoots are probably next. The core concept to this sort of photography is that it is quantity over quality. If you commit to this light, handy gear, then you should be prolific too.
If you want to turn out the high quality stuff, it is a commitment to the financial, time, bulk and weight resources that are needed to pull it off. That gear needs more protection from water, dust, bumps and theft. Just getting it out can be a time priority: everything else is going to stop while the image is made— the setup, the lens, lighting gear, waiting for the light and action and so on.
I remember a guy looking at my 4×5 setup and saying, "Wow, I never wanted to make a picture that much." I think that says it all: how bad you want to take the picture? Are you going on a photo trip on a bike, or a bike trip recorded by photographs? There is your decision maker.