Some website redesign projects I've worked on in the past only launch when the site is 'perfect.'
Every feature has been built and implemented, every page triple checked for content changes and an accompanying call to action. Plus everyone in the company has essentially signed off before launch. It's not to say these kind of projects don't do well, in the end the client is happy, but it means spending months even after the design and template development is done collaborating on actually building the website.
There's nothing inherently wrong about this process since the site does get launched and it looks good and functions well and has all the bells-and-whistles. There's a soft launch to check for any last minute deployment issues and then a big announcement from the company about the new site.
More often then not, however, a smaller, minimum-viable product version of the site could have been launched much sooner. Instead of waiting for every feature to be built, or every page to be updated, or everyone to sign off, the new website design could have been public sooner, reaping the rewards of the new mobile-friendliness or updated branding standards.
There's a number of benefits to launching a new website design sooner.
First, you launch that platform website that you'll be making many iterations and tweaks to over the years and get it out into the light. Making it public sooner can lead to changes in direction if you find a design element isn't working well with your visitors, or even doubling down on something you didn't initially think would work.
Second, your business will benefit sooner from the updated design, which I would bet is responsive and modern compared to your current website, which may not work on mobile, and may be on an old CMS. Your marketing people will be able to make edits more easily, and sales will have an updated tool to show off your products or services.
Making smaller iterations to the site over time, instead of waiting until it's perfect, can also mean a boost to your SEO rankings as Google sees you're constantly improving the site.
Instead of waiting until the site is 'perfect,' launch an MVP sooner and start learning from your visitors to make the right website design decisions for your business.