SEO one page at a time... versus SEO a "website"?

When people google something, they land on one page at a time... a page that has been optimized for a keyword/topic.

Can single webpages rank well, without the effort of optimizing the whole website?

Obviously it would be ideal to do a whole website structure that is well organized and lends itself to internally linking to various keywords, but we only have so much time.

How important is this effortfull work of website architecture, versus spending our efforts only optimizing specific pages?