This is probably not the perfect analogy, because at some point you will have to stop and change the tire. But it maybe if you don’t do it quickly, there will be a much nastier outcome and expense.
The trouble is, you cannot stop the IT vehicle to make substantial changes to processes that would bring delivery to a halt; you have to make changes while you keep going with business as usual.
However, looking at the things that can bring benefit with minimal effort, it is possible to make progressive incremental changes that buy you time from the outset and start you on the journey to greater savings. If the majority of your testing is currently manual, then adopted in the first instance technology that makes this less manual (less effort) is an easy and quick win.
As knowledge is collected and built up from this process, it can be re-used more easily and selectively migrated to automated tests with an immediate positive impact on timescales and effort.
You can keep driving and slowly accelerate. You just need the right technology in the right phases for the right people.
That ERP style application is fundamental to the running of the business and it cost a lot of money to get to this point. It is going to keep costing, so it is worthwhile considering how to lower this on-going cost.
The process of maintaining it relies on a collaborative approach between IT and the business, each sharing ownership just with more emphasis in some areas.
Changes are necessary and inevitable, perhaps even out of your control for Cloud instances, but they create risk which needs to be mitigated by effective testing.
The right technology adds real value to this process and will save time, money, and embarrassment if implanted correctly.
There is a navigable journey to a better place. It does not leap, it is a progressive sequence of incremental gains. It will be worth the effort.