The wire, however, including the account (the routing number can be looked up by your bank; it just saves time if you already have it) is a very specific approach to transferring money in a certified manner. It's older, and has some overhead and history in how it's tracked and managed, if for no other reason than that the funds are guaranteed. As such, there are still fees on it (and that's probably true in most countries, btw, unless you have a balance over a certain amount).
Most folks paying their babysitter $40 aren't concerned about a certified transfer, and assume they will have funds to cover the check when cashed, so they don't need to pay any fees and will just do a regular "check". And I would bet that the banks are working on ways to do a better job of making electronic links to reduce their need to print those checks (for example, perhaps if I keep paying my babysitter 2 or more times, the bank could automatically check the clearning house for the deposited check, and, in the future, autonegotiate a direct link with the babysitters bank and account for payment or something clever like that; I don't know if that would really work but sounds cool).
I'm not sure what the costs are for wiring as it is usually packaged. I pay $30-40/year for Internet bank w unlimited wiring including p2p through phone number (yes guaranteed/negotiated transfer to the babysitter!). Meanwhile cash-paying a bill or cashing a check is probably $10 a pop, simply because banks are trying very very hard to get rid of two things: cash and staff. that makes a lot of sense from a business perspective.
Here, transfers are free and any "paper" business such as check cashing/bill payment has steep fees.
How can your banks provide you with the labor intensive service for free and charge for what is cheaper to provide? Aren't they creating a customer behavior they don't want?