The Basic Landing Page is not fully responsive on mobile devices. See the screenshot attached. Part of the screen is cut off. This was tested on screen viewport size 375 x 667, which is still the second most common size.
I apologize you're seeing this happen with your sign-up form! I would however like to point out our Basic Landing Page forms are the older version that was created prior to our sign-up forms being mobile responsive. Because of this we would recommend using our updated Lead Generation Form instead. Are you having the same experience with this form?
You are correct they do not currently provide that feature. I think that is good feedback for our developers and we are currently tracking customer interest in it. I will make sure they know this is something you want. At this time, the only work around is using the landing page as you have done. I do apologize for any inconvenience.