Current mobile OS's (iOS and Android) do run without a pagefile, in order to cope with the crappiness of inbuilt eMMC storage which would quickly wear out as the pagefile got rewritten. Theoretically, well-behaved applications are supposed to checkpoint their own internal state when signaled by the OS to do so, since this ought to be more space-efficient than the use of a pagefile; in practice, almost no applications actually do this properly.

For what it's worth, Linux is a lot more parsimonious in its use of swap space than Windows, given very similar hardware and use cases.