What's this 15 bill pay limit thing you're talking about? It doesn't sound right. Can you pay your bills online, and that won't count? Are you talking about writing 15 checks? I've never heard of such a thing. Who charges you to pay your bills?
Lots of banks used to do this until they figured out people did not want to pay for that. It seems unusual now though.
I used to make regular online transfers from my main bank to another bank. My bank decided to charge a whopping $3 for that (like an ATM fee) so I just started initiating the transfers from the other bank! No fee for that.
As for the 15 limit, lots of banks have a low limit on checks or things that are not electronic. But it seems very unusual to apply it to electronic transfers. I think they are just being greedy.