The notion of a computer system having an accurate idea of the "real-time" state of apartments available for rent requires you to actually know what inventory is available before you can integrate it with the listing website.
That said, apartment pricing is also supposed to be opaque -- bigger communities appear to raise or lower prices algorithmically like airlines (raise the price of available units right before existing leases are up; lower the price when nobody is looking to rent; account for how much rent for "comparable" units has gone up; sell cheaper, less desirable units before more expensive ones).
In most cases the phone call is the bare minimum you should be doing -- you want to go visit a community in person to get a "feel" for it anyway, and to let them do their sales pitch (what are the amenities; what is the best, most expensive unit you can afford versus cheaper ones, and what trade-offs are there; etc).