I too am just starting out and wondered the same thing myself. I found a few PMs that process applications and take payments online only. I quickly dismissed those PMs because of the same concerns @Joe Butcher raised.
I'm beginning to see it's not uncommon for some of the better cash flowing properties in DFW to be in areas where most (if not all) of the tenants mainly speak Spanish, so it's something one must become accustomed to dealing with in such areas.
But I have to agree with @Steve Babiak. Anytime I have spoken on the phone with someone who does not speak English very well (if at all), almost always has someone around them that will interpret for them, or will call you back when they do.
Another thing to consider... Place yourself in the shoes of a tenant. If you were out looking for a place to rent while driving around, is it easier for you to immediately whip out your phone to dial a number, or to try accessing a website? Sure smart phones have internet access, but realistically, it's much faster to just call a number and leave a VM than to wait for a page to load on a phone. Most folks will just take the path of least resistance. Just food for thought.