This is pretty much never the case, and more often than not the company is successful despite those process, not because of.
Many processes evolve on an ad-hoc and as-needed basis, with some tweaks here and there over time as the company grows and staff turns. You eventually reach a point when no one can remember how a process came to be, or why Sarah has to export four files from three web interfaces and copy/paste data across two Excel files to send to John over in accounting that was just trained last week on how to use this file to true up actuals.
There's only so many ways a company can track inventory, or manage purchase orders, or calculate product costs, or represent sales order and invoices. An ERP acknowledges that a vast majority of businesses operate with the same set of industry-specific operational primitives, and businesses have learned that it's both more time-and-cost effective to adapt your business to the expectations of the ERP than the other way around.
In the rare case you're doing something novel, you can still build your bespoke solution on top of those existing ERP primitives without having to re-invent how the numbers come together so your company can spit out the three financial statements.
SAP does not need to touch the "unique" detailed processes that makes a company great, nor it's culture. But if you e.g. manufacture a product, the design process can still be relatively unique to your company, but most often, the manufacturing processes should follow the high-level blueprint of manufacturing companies.
If its the former, than conforming to SAP is giving up what made you good. But if its the latter, then conforming to SAP is just making the basics more standard and easier to maintain.
No executive wakes up and things ‘this is a great day to pour 500M down the drain’.
Standardise the mundane (with an ERP, with minimal customisation) business processes so your company can focus on innovating where they have true competitive advantage. This is the recipe for a successful ERP implementation.
Telling that losing your uniqueness and being like “everyone else” will actually become your competitive advantage is something that only SAP can come up with.
If you already grew big, you won't grow bigger by adopting SAP. You can stagnate at best, as shown a million times in the real world. Companies that still want to grow just don't use SAP. Period.