I'm not sure how much this could boost Steemit growth, but it could be an attractive and distinguishing feature.
There are loads of cool apps build around the Steem blockchain, such as:
- SteemWhales to show loads of stats
- Steemviz pending payouts shows what you will earn over the next week
- Dead Followers to see how many of your followers are active
- Steem chart to check the prices
- Steemvoter to automate your voting
How about if these could be integrated into the main Steemit site? If you are using a PC with a wide screen then there are blank areas on each side that could be used for apps. We could each choose the set we want to see or at least have easy access to. Some apps need your username and that could be automatically passed. If an app needs your active or posting key then it may be able to do that with minimum compromises to security. Obviously that implies a level of trust, but we have the transparency to see if our account is being mis-used.
So why would app authors want this? I think it could gain them more rewards for their work. It should be quick an easy to send a payment of your choosing to the creator. Part of the app store would be a Tip button that takes you to the transfer page with the recipient name filled in. There may be a market for premium apps that you have to pay for. Steemvoter plans a premium version with more options.
The result of this would be a customised Steemit experience and a more active developer community. I don't see many sites that offer this.
Update: @liberosist reminded me of Steem Tools that is linked from the menu on the right of the Steemit page. I meant to mention it, but forgot. This is effectively an app store, but having something more integrated could open new possibilities. I'll have a look to see what's been added recently.

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