If your entire business has one single focus, then... maybe.
The majority of businesses offer a number of products, services and brands that will each need their own representation online. Additionally, your business should have unique factors that will help you stand out from your competition, your website is the perfect place to surface this when potential customers are evaluating their options.
Landing Pages are designed to have a single focus and call to action aligned with your advertising efforts. They don't allow for potential customers to browse and find out more about your business, which is important for forging and maintaining longer-term relationships and closing sales.
The common practice for leading businesses is to have a website which supports existing relationships and brand with supporting Landing Pages to drive straight lead generation or qualified customers into more complex sales funnels.
So in summary, no, in most cases you should not replace your website with a Landing Page.