Stripe Extension: use, or copy Stripe Checkout
Stripe has put a lot of data and experience into their checkout product: https://stripe.com/blog/checkout-new-features
It would be really great if WooCommerce could just use their checkout when only the Stripe gateway is enabled.
If that's not an option for some reason, you should really consider trying to make the WC checkout page more like theirs: as simple, straightforward, and easy to use as possible, plus fully mobile compatible with responsiveness and touch-friendliness. The checkout page and process is still a big stopping point for many clients.
This was added way back in version 1.5.0. Been around a while and it’s very solid (and pretty). :)
I work at Stripe on the Checkout product (firstname.lastname@example.org). I'd be happy to help in any way to make this a reality!