Would it be better to show a calendar picker by default instead of an input field with pop-up date picker?

On a travel site which is for Desktop, iPhone, iPad too, would it be better for UX and Accessibility to show the calendar itself on page by default

Like this

Or the most popular way, a input box with calendar link which opens a calendar on pop-up.

I was just thinking that it would be good for a user to see calendar itself with current date. It will save one step of clicking on icon and opening in popup.

And I think a Pop-can be also be problematic on Touch screen devices and to screen reader users.