Interesting debate, and suspect there is no right answer in all cases.
SfS mentions that commercial arks don't have floors, but most outdoor commercial setups will be on sandy soil, not the clay that we have.
Commercial setups will also move arks more frequently using front-loading tractors, and not want the bother of internal cleaning. Small setups may not have the moving equipment and can take the time to clean floors, not an expense a commercial set up can afford.
Commercial setups tend to be high density and quantity, so potential disease is more of a problem - our two commercial arks are made from steel frames and ends with twin coverings of curved sheeting, allowing good cleaning and disinfection. The majority of smallholders have low stocking densities, and wood ends on the arks, so a wood floor does not really make a deal of difference in adding risk where wood is already present and stocking density is low.
All our arks have floors, and we have never had a vermin problem.
SfS is correct that some ark manufacturers use plywood for flooring and this can cause slips and strains when wet, so we don't use ply, but if you have ply it needs to be well strawed to prevent this.
Didn't really understand the draft argument, so can't comment of that other than I see no reason why a floored ark should be draftier than one that sits on uneven soil - if you add straw both would surely be the same?
I also don't see why having a floor means you can't provide straw for a farrowing sow to nest with - we farrow on concrete in sheds and have no problems in the sows nesting - one is doing it right now.
Nor do I agree that a solid floor increases crushing over straw one - doesn't matter whether you are lying on the bedroom floor or on a silent night mattress, you'll still be crushed or suffocated if something several hundred times your size and weight sits on you.
Many of our arks have Pallet floors - these are made from taking the planks from one pallet and nailing them over the gaps in another creating what is called castle boarding sort of viewed edge on _-_-_-_. These are loose fitted in - ie you just put 4 to 6 or so (dependant on ark size) in the middle, rather like having a large rug in a room rather than fitted carpets. The pigs don't mind the castle boarding at all, and with a little bit of straw it disappears anyway. This lifts the pigs out of the mud, and off cold ground, whilst letting you easily clean by lifting the ark away, either with our tractor for the heavier ones or with the carbery arks we have some of you just flip the ark away.
Whilst SfS points out some valid reasons for not having floors - time, possible bacteria, possible vermin, and these should be considered, their are positive factors such as rasing the pigs up from wet ground and in winter raising pigs up from frozen ground that make it worth considering.
However as I said at the beginning, there are no universal right answers and everyone should consider all the arguments. For us floors are needed, and have no proved an issue.