Could not this be done here in steemit within the posts.

It actually is done here on steemit with posts, the website itself would be powered by the steem blockchain, so it would mirror the content. The @bounty bot itself is posting all activity which appears here on the site.

The difference here I think is trust. I'll use you as an example, hope that's alright :)

If you were to start a bounty right now, and I ran into your bounty post, our interactions wouldn't be based on a level of trust. I personally don't know you, and that might impact my giving to your cause. Maybe I thought you had a great idea and wanted to add 500 SBD to the bounty. I'd need to trust you for this.

Even going one step further, would I even want to up vote your post? Maybe you're running a bounty you know that no one will accept just to farm steem power. I might even question upvoting your post, regardless of how noble your cause is.

By pushing the trust factor off to a bot, it eliminates these concerns for me. I know it's not just you trying to increase your influence, I know you're not running a scam (because you're putting money out for it in advance), and I know I can trust the bot to not run off with the rewards, which an unknown author might.

I post a bounty, a hunter accepts in the comments, payment is made in another post once the work is done (or a trusted steemit user acts as escrow), others promote and so on?

In the end, you absolutely could do this even if this bounty system exists. Do you want to? Do you have enough trust within the community to have others contribute and fund your bounty? Do you think it would be successful?

It's possible you could, but a system like this I feel takes away a lot of the friction.