What is the flow that you're following when developing API application?
I never go full API application between Laravel + Vue. The problem is it's time consuming to develop web app with API. For example, the form validation is extra work when using API + Vue.
It doesn't really take much longer to do those kinds of tasks either when you use libraries like axios to reduce the amount of code you need to write. You just need to find a good work flow to get into and you won't find it to be much extra work at all. On a project I'm working on, I have mixins I have made for vue that further help with ajax requests and forms by helping me normalize certain aspects of the request and making it so I don't have to repeat myself very much.
What about CRUD is time consuming? You really don't have to write much code in laravel to save/update/delete items, especially when you are using features like route model binding and form requests to validate your data.
@wilk_randall Actually, In one of my project I make use heavily of npm library from validation to customize component between bootstrap and vuetify and use a vue-recaptcha. Still, the work flow is suck. With vue-recaptcha, I need to go back and forth between server code and js code to make it behave correctly. Especially when their are a lot of CRUD operation involve where a small change will require go to different file just to track the file that I want to change. I wish people share their work flow online.