Ordinals rely on satoshis being non-fungible and trackable. So yes, ordinals break when you consider that:

1. Someone can swap a bunch of sats for some other bunch of sats just as easily as we can swap dollar bills and pretend that nothing happened.

2. A Bitcoin transaction can pay a bill in the first output and return change in the second, but it can so return change in the first and pay on the second.

With the existence of coin swaps, coin joins, lightning payments, pretty much anything that isn't "ordinal compatible", ordinals break.

This is why they are so dangerous: they encourage "the people" to settle on invisible limitations so that the rest of us can be othered and then labelled as insignificant, abnormal and criminal.