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There is not a way to set a default subscription view however this -https://community.tableau.com/ideas/8627 Ideas is very close to what you are suggesting. I suggest creating a new Idea and promoting the idea here. Be sure to vote on your own Idea as the vote is not automatically recorded for the creator of an Idea. This is an excellent Idea that I agree should be a part of the product.
The subscription image that is sent depends on what mobile layout is selected when you publish. For example, if you publish while on the phone view, subscriptions will get the phone view. To change it, republish with the desktop layout or tablet layout selected.
Hope this helps,