What you are describing is called "refactor" not "rewrite". Incremental changes that use existing code don't allow for great changes in the architecture.
I'm not against rewrites, sometimes the company grew so much that you need to start from scratch and rethink given your current knowledge. Or you started with a low fidelity prototype and you rewrite to create a production ready feature, without the crufts in the design you had when you started.
It's also possible to incrementally change the architecture. It doesn't have to be a Big Bang.
Edit: refactoring is usually considered to be done on existing code base. I really mean thowing a whole component away and re-doing it from scratch. The components need to be small enough though, that you can deliver them to production within 2-5 months.
I'm not against rewrites, sometimes the company grew so much that you need to start from scratch and rethink given your current knowledge. Or you started with a low fidelity prototype and you rewrite to create a production ready feature, without the crufts in the design you had when you started.