It's not that desalinisation is "hard", you could just boil the water for example. It's that it's extremely energy intensive and complex to setup a process that's both repeatable in industrial quantities and can produce enough flow to satisfy demand.

It's not difficult it's just expensive and energy intensive, and frankly boiling water is both cheaper and easier and we've had lots of experience doing it in massive quantities since the steam age and it works great and gives off steam or hot water which can be used for lots more stuff like heating and even power generation. Ice is almost useless in comparison.

As for why you can't freeze salt into ice, they don't mix. It's like trying to mix oil and water. Technically, if you get the ice really really cold and mash it up with some equally cold salt you could make some kind of mixture of ice and salt and maybe even compress it together until it forms a solid mass again, but it's not saltwater ice, it's just salt and ice mixed together like oil and water. They may appear mixed, but they don't mix, they don't dissolve into each other. Ice's crystal structure does not have anywhere for the salt to go and the salt's crystal structure doesn't have anywhere for the ice to go they're not compatible in any way.

It's harder to freeze salt water then fresh water, do it's not economical.

The most energy efficient method of desalination i believe uses a membrane and pressure to get the fresh water to one side.

But these aren't even the biggest issue. The real question is what do you do with the left over brine? Desalination is not 100% perfect. You're left with fresh water and a salty sludge called brine. It's extremely difficult to dispose of without causing environmental impact