There could however be a way to circunvent the problem of space filling by Ordinals and other data-spam transactions: create a special discount for simple payment transactions which only consist of inputs and outputs with the simplest possible P2WPKH script.
Currently we have a two-tier discount scheme due to Segwit:
Tier 1: Segwit witness data (weight in vBytes = weight in bytes)
Tier 2: All other transaction data (weight in vBytes = 4 * weight in bytes)
We could advance to a three-tier scheme:
Tier 0: Simple payment transactions (weight in vBytes = 0,5 * weight in bytes), i.e. they would have a weight of half of the Segwit witness data*
Tier 1: Other Segwit witness data (weight in vBytes = weight in bytes)
Tier 2: All other transaction data (weight in vBytes = 4 * weight in bytes)
The main problem I see with this approach is that effectively penalizing smart contracts and similar transactions (such as LN and sidechain related transactions, as you already pointed out), is throwing the baby out with the bath water.
Also the fact that Ordinals inscribers (inscriptors?) appear to be largely fee insensitive would probably make any form of monetary penalty largely ineffective.