Having an in person or live conversation is almost always more costly. Yes, it likely cuts down on the number of miniscule requests that you will receive, but you are likely to get a large number of those via telephone, unless you don't offer that as well, which would be impossible for offsite property managers.
So, in short, yes, I agree with you that the number of silly requests may go up, especially initially. However, to counter this, sorting them takes all of 5 seconds a piece instead of 5 min to listen to them ramble on the phone, the benefits of online rental payments saves you time and money, and the instant organization that comes from having this all flow into one system is in our eyes, priceless.
Thanks for your valuable input!