That's all true - but at the same time theoretical approach disables your ability to see the real world
When you have a bunch of particles (in liquid or solid), each one occupies some space, they don't get to close to each other. So you may assign some kind of diameter to them.
If you have a hole in the crystall lattice it can be occupied by some particle (or atom) that is not part of the lattice - it just have to be small enough to fit (clathrates for example). This size is some kind of diameter too.
You may say it is not possible to calculate diameter for any particle because particle 'never ends' (and theoretically you are absolutely correct), yet you have somehow name the size of the particle observed when it interacts with others.
What about diameter-which-greg-refuses-to-call-diameter?
This is similar approximation to the one used when talking about orbital shapes. Orbitals 'don't end' too, yet their shapes are known to every chemist.