Note: When you introduce an idea like this and say "we are building X", it's good to explain who "we" is. The advice people give you may differ based on their perception of how experienced you are, what skills you do/don't have access to, etc.

There are various apps that handle different elements of what you've proposed. Momentum lets people set up recurring donations based on external events; EA Funds allows recurring donations; apps from outside the EA community have a variety of features.

Regarding a few aspects of what you've said here:

There will be a leader board of different people's donations.

Generally, people are reluctant to publicize their donations, with the exception of certain very wealthy philanthropists and a few unusual "normal" donors. I can only think of a few dozen people in EA who publicize their donations, and we're far more interested in doing so than the general population. Reasons this is rare:

1. Broadcasting one's giving, is generally frowned upon; it reads like bragging to many people (just as it would seem like bragging to talk about how much you spent on a new car).
2. If someone tries to broadcast their giving, it also may seem like they're giving mostly for attention rather than to help others.

Within EA, I think these reactions are uncommon, but I'd expect them to be quite common outside our (very small) community.

Keep in mind that, despite Strava et al., there aren't (to my knowledge) any popular apps that share amounts given. Even every.org, which is trying to bring a modern social networking mindset to charity, doesn't seem to share amounts (though maybe this is an option they allow?).

The force of social disapproval seems likely to overwhelm most of the benefits people would get from e.g. gamifying their giving or signaling their altruism.

I publicize my own donations very carefully; my personal donation page includes several paragraphs of explanation, and I only post about giving on social media if I have a very good excuse to do so. I think most other people share this mindset.

Why does EA not encourage givers to share the fact that they have donated on social media?

"EA" doesn't really encourage anything; individual organizations and people in the EA community encourage various things. Often, "X not being encouraged" just means that everyone is putting energy into encouraging other things and hasn't gotten around to X.

Some people probably strongly believe in sharing donation info on social media; others probably oppose it. I don't know what the consensus is like, but I've set up an EA poll to get some initial data.