A company that cares about eroding trust in third-party repairs shops getting blamed for ripping off their customers when the battery still reports as broken.
The Right-to-Repair discussion often ignores a key problem companies have: figuring out whether a device is under warranty (i.e. whether they’re obligated to repair the device for free) when it’s submitted for repair.
Some repairs make themselves obvious, and so make the removal of warranty obligation obvious. Other repairs—like third-party battery replacements, done following the Apple process for repair and with Apple OEM components—make the warranty status of the device illegible. If the phone accepted a new Apple OEM battery without saying anything about it, the user might be misled into thinking that the device is still under warranty. But it’s not. It’s been repaired by a non-authorized third-party. It’s no longer Apple’s fault if the device breaks, because that third party may have screwed things up inside the device in any number of ways.
This is, in a sense, a “chain of trust” thing. It’s the same reason Chromebooks have that on-boot warning in development mode. The user needs to be aware that the chain of trust between the OEM and the end-user has been broken; and that, when that happens, anything may potentially have been done to the device.
That’s not to argue against Right-to-Repair. Non-authorized third-party repair shops should have every right to operate as businesses, and end-users should have every right to do business with them. But Apple also should have every right to warn users that the chain of trust has been broken—because it has. The user knowingly broke it themselves! (And, of course, Apple shouldn’t have the right to misconstrue breaking the chain of trust as anything more than that. The battery health is unknown because it’s not an Apple-certified repair, certainly; but that doesn’t mean that the battery is bad, and it would be anti-competitive to claim that.)
I get where you are coming from but this isn't so cut and dried, as incompetent repairs are certainly capable of damaging or destroying other components. Someone I know once unknowingly messed up an antenna in the process of replacing a phone battery with an after market one, which caused all sorts of odd and intermittent symptoms with communication issues. Why should a manufacturer be expected to deal with that under warranty?
Part of the problem with consumer electronics is that they aren't really particularly designed to be serviceable, let alone user-serviceable. So it's not like a car manufacturer saying they'll refuse to warranty a rear shock because you changed your own oil or whatever.
I'm a strong supporter of right-to-repair, but I'm not convinced that should extend to forcing user serviceable designs where there is an actual design tradeoff. On the other hand this is pretty hard to prove - maybe all you can do is go after user-hostile design changes that serve no other purpose.