Sadly, a lot of current software does behave like it owns all of the RAM on the machine. But modern browsers are particularly bad, and it doesn't help that you need the web for so many things today. With browsers I'm not given much choice.
> This is what virtual address space does, it's pretending that each program has access to any place in the memory.
No, not at all. It's just handing control over to the operating system so paging can be handled transparently and programs can't overwrite each others' memory. Programs still have to acknowledge and respect the fact that memory is a finite resource, and they can't have all of it. That's how it has always been, a virtual address space doesn't change the fact.