Companies like GoCardless exist for this reason. Problem is that fraud is still a thing and cash payments over the internet aren’t possible.
[1] https://www.interac.ca/en/consumers/products/interac-debit/e...
I don't know if the merchant fees for Visa Debit are any different to using a Visa credit card.
When at a physical point of sale, a Visa Debit card is processed over Interac rails, and I believe Interac interchange prevails. At one point back in 2009 Visa was going to set up their own debit network in Canada, but as of 2010, my understanding is they gave up on the plan. The value add from the Visa Debit rails is for international online purchases, for phone purchases and for international point of sale purchases, neither of which are well supported by Interac-only cards.