Over the years, I have done both - no "floor" and full "floor". In good weather, usually just that tarp under the bedroll and gear. Wet/muddy weather I used more tarps - both to keep things dry, but also to cut down on "mud" from foot traffic.
Winters were different. I took extra steps to "insulate" the ground from the inside of my tipi. I would put down a waterproof tarp, and then cover it with some heavy woven carpet padding. That "insulation" of the floor helped our comfort, but it also helped keep the ground from thawing out and turning to mud. There were several winter camps where all the snow melted during the day and we had mud everywhere. But when I struck camp, I left a nice "donut" of froze ground/snow where my tipi had been - just the firepit area melted and melted all around the outside up to the floor covering. At one camp, some guys who were staying a couple extra days then moved their tipi over onto that ... high and dry spot.
It's all a matter of your personal choice, and the level you wish to achieve within your camp as to gear and set-up. Mud/dirt/wet is all too accurate, but some steps can be taken.
Just my humble thoughts to share. Take them as such.
Mikey - yee ol' grumpy German blacksmith out in the Hinterlands
p.s. I ran with a 16' RK Lodge for many years during that "mountain man" period. Traded it off years ago. But now I picked up an old 18' cover/liner to "play" with. It's almost 30 years old and needs some ... patching. I'll cut some select cedar poles out of the deep timbered hillsides around here. It will be nice to "go round" again - in selected areas/events.