Such a system does exist for Canadians but it is not as robust as Paypal.
The closest is the CDN Interac email money transfer system offered by the major banks. It was pioneered by Certapay and has similarities to paypal.
That is what was discussed right above your post.
You could maintain your own merchant account for online payments, there is a lot to discuss on this topic with risk/fraud and reserve account balances imposed by the underwriting merchant bank being among the most important/obvious business drawbacks.
There are pluses but this is a very rich topic that requires a very deep understanding before you can be sure you have made the right decision for your online business.
I am personally not into Paypal bashing, they have done amazing things to accelerate the growth of worldwide online commerce which I have personally benefited from greatly. They are far from perfect, and have done very questionable things, and it is sometimes difficult for non insiders to understand why but I would rather have them than not have them, that is for certain.
Also when you said you wished a real bank would get involved in the Paypal market-space you did not specify you meant a Canadian Bank (as you now say), that is why I informed you that Wells Fargo is the underwriting merchant bank for Paypal and they support them enormously. With a Market Capitalizaton of just over 100 Billion US (approx 3x larger than the Royal Bank of Canada, and approx 5x larger than The Bank of Montreal) they certainly qualify as a "real bank".
I will also share with you that an extremely well funded Citibank subsiduary tried to enter Paypal's market space and was smashed to pieces by Paypal's market dominance.
http://www.c2it.com/ The only 3 substantial threats to paypals amazing rise have been 1) Would eBay refuse Paypal payments on their platform and build one of their own by building on BillPoint/eBay Payments or buy Paypal? (the answer to that is of course they bought them); critical question given that historically well over 50% of Paypal revenue has been generated by transactions that originated on eBay. 2) Regulatory bodies (includes governments & credit card companies 3) controlling fraud/chargebacks and being able to turn out a net profit at the end of the day in light of these metrics. They discovered maintaining a fraud rate under 0.40% was essential to profitable operations. This was achieved through investment of hundreds of millions of dollars in the creation and continual evolution of IGOR, which is paypals proprietary software "eye in the sky" or "big brother" and named after the guy who caused them trouble in the early days.
Thanks for making this a little more interesting now. I was getting bored by repeating myself to ensure it was sinking in and to drive away false information on this important topic.
Troy