When determining the best towel bar height for your space you need to take into consideration how your bathroom is laid out sometimes the placement of outlets and light switches can affect things.
Bathroom door height off floor.
I prefer to run shower enclosure glass to the full ceiling height with the door just slightly below to allow for a free swing as i did in the bathroom shown here.
The standard i use is 1 2 over finish floors 3 4 is acceptable.
The additional room allows for a 3 4 inch top jamb a shim.
At the back of the sink or toilet the ceiling height can be as low as 60 inches.
That is a lot of room for unlevel you have there.
The height of common doors is 6 feet 8 inches.
To fix the issue the doors need to be removed bottom of the jambs cut and reset the door.
A 450 millimetre wide fixed panel and a 600 millimetre wide door panel work well for a typical 1500 millimetre tub.
I just took a quick look at some of standards and regulations governing door undercut which is the distance between a door and finished floor as opposed to clearance which is door to sub floor.
Toilet bathroom building codes.
I have never seen a door set with that big of a gap unless it was to get past floors that were not level.
The front of the toilet needs to have at least 21 inches of clearance.
The standard recommendation for towel bar height is 48 from the floor to the center of the bar i tend to hang mine between 44 48 high.
The shower door needs to have an opening clearance of at least 24 inches.
So says the building code.
The standard height of the rough opening for a door is the door height plus 2 5 8 inches.
The awi gives no minimum but a maximum of over 3 4 is unacceptable.
Interior door height off floor.