I think all of them here in Canada (unless you have some special merchant account). The banks all claim that you won't be held responsible for any fraudulent use of your account online. They wouldn't be able to claim that if you could do irreversible wire transfers.
I live in Finland, and the whole concept of not being able to send wire transfers from your online banking (or even a phone app) sounds utterly ridiculous.
This seems to be the norm in most of Europe. AFAIK the big US banks let you do wire transfers online too.
Where do you live?