https://www.nih.gov/news-events/news-releases/induced-labor-...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4049989/
Normally though, induction happens because there is some problem or because the pregnancy has gone past the due date, and in these cases your risk of a c-section is already elevated.
This review finds the rate is actually lower after induction, contrary to popular claims:
induced labour happens in so many different ways, that broad statement is not going to fly.
Also there are many way to induce labour, none of them are quick. Some take a few hours, others days.
For example a "sweep" is where someone goes in and stretches the cervix, with their hands. There are pessaries too. None of it is quick.