1) Other SMTP servers like Gmail won't work with Godaddy Shared Hosting
Virtual and Dedicated plans have 1000 relays per day limit. Additional 50 relays per day per month costs around 3 USD.
If they allow third party SMTP server connections no one will use their Email plans. That's why they are blocking it. Compared to Google and other companies, giving free emails with massive storage, unlimited relays and other features, GoDaddy's email plans are pathetic.
I'm planning a workaround for this problem. My idea is to host a PHP application in a server where SMTP connections are allowed and call this application from GoDaddy sites. If anybody have better ideas, other than moving out from GoDaddy, post here.
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