Question about Mobile On-page SEO

I saw web page only considering mobile environment. I mean, text placement, image placement, and paragraph placement were created only considering mobile devices. Then, do such mobile pages eat penalties for online SEO awards? Is there no problem?

It might perform badly on desktop if the URL is the same or engines might just ignore ranking it there completely. On mobile it should do great.

Normally, most websites should be optimized to appear and perform well on both devices. Website may get penalized if it's not optimized for one or the other environment. For example if content is going offscreen, or whatever makes the website unusable in one environment.