It doesnt even need to be lower cost, if they understand the business. We compete with a lot of startups (im not at a startup) that build their entire case on 'you are our entire client base, whatever you want, we can build' where our approach has to weigh up all client requests and build towards what we think the best overall solution is going to be.
For those clients its beneficial to them to go to someone new that will cater to their exact wants