You don't need to delay a launch
Launch your projects
I've seen this happen many times when working on internal and external website projects. Key stakeholders become obsessed with perfection as you get closer to launch date. You may have completed all of your dev work, run all performance and responsive checks.. but there is a never ending list of changes.
And so you get left with two options. Commit to every little change that is requested and go way outside the scope of the project. Or put your foot down and stick firmly to what was outlined.
You need to be able to draw a line when completing your projects. Critical issues and immediate fixes take priority. But you need to consider time and value when dealing with extra requests.
Can I complete this quickly?
Can the client benefit from this if we do the work?
What impact will this have if we don't ship this suggestion?
In most cases of large requests, I would push for them to be handled after launch. I've seen projects delayed for months over small details when they could be published and start capitalising on SEO and lead capture improvements.
The best part about building a modern website is the fluidity and flexibility it offers. Deployment pipelines make it easy to push changes and serve new experiences to your users in short amounts of time. A good developer will automate this so updates can be rolled out within minutes of approval.
So I talk to your clients and work out if changes outside of the scope can wait. Let them know they can start benefiting immediately from improved SEO and lead capture techniques. Changes are quick to roll out, and they won't be forgotten after launch.
It's not the end of the world if the website isn't perfect. What matters is your new website starts working and performing better so your client can reach their goals.
And hey, if they ask for hefty changes after launch - you bill them for it.