The problem with a skinny is it cant go on the front I'm told, so if I get a front puncture late at night in the rain I've got to take one off the rear to put the skinny on then put the one from the rear on the front before I can go any further. Nightmare!!
You are quite correct. So you have to weigh up the options.
a) A skinny = Can't use on the front, maximum speed no greater than 50mph and must be changed ASAP
b) A Steel 16" + appropriate sized tyre = Heavier, must match fitment and offset. Can be used on the rear
c) An alloy + appropriate tyre = Lighter, must match fitment and offset. Can be used on the rear
d) Run flat tyres = Expensive