I understand all the concerns expressed but do not think that there is much of a problem here.
You don't treat timber furniture with intumescent paint but you can use timber that can be categorised as being a material of limited combustibility (i.e. a relatively dense hardwood, see ADB or other sources).
Guidance allows a smallish reception to be situated in a staircase when the building has more than one staircase, so provided that the furniture presents no greater fire loading than such a reception area then we remain, in essence, code compliant.
If you wanted to put furniture in two or more of the staircases then I really cannot see the problem in a well managed building. If there is a fire, it will only involve one staircase, it's not going to leap from staircase to staircase. The risk of arson would need to be considered here.
I understand that the building is full to capacity and that all the stairs are required for evacuation. I also understand that if the fire is in one of the staircases then there are a restricted number of escape routes and occupants will take longer to clear the floors and reach a place of 'relative safety'. But this is not important because the fire is enclosed in a staircase and people have at least half an hour to clear the floors in an environment protected from the fire, longer if there are lobbies, longer still if it is a firefighting stair. The floors themselves are places of 'relative safety' if the fire is in a staircase. Confidence in the compartmentation is required for this argument to be valid. Also, of course, the building must not have pressure differential systems installed.
If the staircase has disabled refuges in it then don't use them, use other ones.
If the relevant staircase is a firefighting staircase then this makes little difference.
I am slightly concerned that people can pass through some of the storey exits into the staircases and have the door lock shut behind them. This is not a good idea in any building and has implications for means of escape and for firefighting. I deal with many large multi-tenanted buildings and rarely come up against objections to having all the doors unlock on the alarm. There should be even less reason to object if the building is all occupied by the same organisation. If there are good reasons to have doors remain locked then specific solutions should be put in place to deal with each case.
Care should be taken to ensure that the furniture does not obstruct escape routes and that other more combustible items do not creep in. A daily check should be sufficient.
Yes, the building has to be well managed, yes the locking door issue should be sorted out and yes, we would really prefer it if the furniture didn't catch fire so it should pass the 5852 cigarette and match ignition tests and generally comply with the furniture, etc, regs but otherwise I see no problem.
Finally, you won't be setting a precedent by allowing furniture in the stairs, there are thousands of safe buildings that already have small amounts of controlled fire loading in staircases.