I've come to realise that realistically, platforms -do- change, and eventually you will need to either commit to a rewrite (even if you choose to do it by spinning up a whole new company like Freshbooks did).
As an example, a SaaS app from 2010 might have been barely responsive, might have been put together with jQuery, and the backend might've been written in a framework that died off in the meantime. And while you can do a lot of little improvements and refactors here and there, ultimately the foundation on which you've built your system gets to a point where it slows you down more than it benefits you, and there's no real way forward.
The stories in the article make me think that the old adage of "never rewrite" is really more like "eventually you will either rewrite or die".