The purpose of software changes as it ages. When we first write something, we're doing it quick and dirty, trying to validate that the core idea is good. We might call it a prototype, a proof of concept, and early alpha, beta, or even 1.0, but the commonality remains: the software has been written with speed and getting the core of the offering right. This is true whether the core is an algorithm, business process, market hold, whatever.
Once we get through that first phase, though, it's time to build "real software". This is the time you build the software you can grow on. All those things that got skipped in the first phase - error handling, monitoring, administration - need to get put into the product.
With product life cycles being what they are, that frequently turns into "hardening" the prototype. Basically, engineering is going to go off and add administration, and configuration, and error management, and scaling capabilities. Engineering probably says they want to rewrite at least part of the system, but gets pushed (or walks themselves) into the idea of hardening.
Bad idea alert!
"Hardening" is building something that looks like this:
Looks nice on top. Pretty shaky down below.
"Hardening", you see, is a myth. Way back when the team first built the prototype, they either "built it right" or they didn't. They either set up robust deployment, included monitoring, got their configuration and logs into a good location, or they didn't. If they did, then you're not having the hardening versus rewrite conversation at all. If they didn't, then you need to do a rewrite.
"Hardening" is a compromise that leaves you with baggage, slowing you down over time. The symptoms vary. Maybe you have a production system that you can't shut down because no one knows how it was deployed but it's functioning (for now). Maybe your releases are high risk because you have to change configurations in code. Maybe you don't have monitoring, so you only know about downtimes when your customers call (whoops!). Maybe the system has a lot of errors, and consumers are confused, creating a burden on your support or dev team. Whatever your particular symptoms, you're seeing the effect of trying to take a prototype (or alpha) and make it into software that will serve you at scale.
There's no shame in rewriting software. It's not a bad thing to throw out software once it has accomplished its purpose. If you wrote a prototype and it showed that your core algorithm worked, great! It has done what it needed to do. Time to retire it and write the software that will implement your core algorithm at scale.
So don't "harden". If you can proceed with what you've got, then great. If you can't, bite the bullet and rewrite. It'll slow you down in the immediate term, but it's the right path to long-term velocity.