> When we talk about future improvements, there could be even bigger problem with ordinal numbers: what if/when we introduce some Monero-like system and hide coin amounts? (for example by using zero satoshi, because we have to use something that will be backward-compatible). Zero is quite interesting amount, because it means "skip amount checking for old clients". That can be used in many ways to introduce many protocols (and also to add fractional satoshis on-chain, because 0.4 satoshis could be represented as zero), so if that amounts will be simply ignored, then I wonder how it would be possible to connect some future protocol based on that with ordinal numbers.

Ordinal numbers are inherently public, so it seems reasonable that they don't work with transactions that are private or have obfuscated values.