It isn't a question of 'some lite clients' -- I am aware of no
implementation of these kinds of measures in any cryptocurrency ever.

Doesn't mean there can't or shouldn't be a first. :-)
 
The same kind of comparison to the block could have been done with
BIP37 filtering, but no one has implemented that. (similarly, the
whitepaper suggests doing that for all network rules when a
disagreement has been seen, though that isn't practical for all
network rules it could be done for many of them-- but again no
implementation or AFAIK any interest in implementing that)

Correct me if I'm wrong, but I don't think it's true that the same could be done for BIP 37. With BIP 37, one would have to download every partial block from every peer to determine if there is a difference between them. With BIP 157, you only download a 32 byte filter header from every peer (because filters are deterministic), and using that commitment can determine whether there's a conflict requiring further interrogation. The difference in overhead makes checking for conflicts with BIP 157 practical, whereas it's not as practical with BIP 37.
 
Sure, but at what cost?   And "additional" while nice doesn't
necessarily translate into a meaningful increase in delivered security
for any particular application.

I think we might be speaking too generally here.

Sure. The security model that BIP 157 now allows is that a light client with at least one honest peer serving filters can get the correct information about the chain. No, this does not prevent against total eclipse attacks, but I think it's a much stronger security guarantee than requiring all peers or even a majority of peers to be honest. In a decentralized network that stores money, I think there's a big difference between those security models.
 
But in exchange the filters for a given FP rate would be probably
about half the current size (actual measurements would be needed
because the figure depends on much scriptpubkey reuse there is, it
probably could be anywhere between 1/3 and 2/3rd). 

This does not seem right. Let's assume txids are removed because they are not relevant to this particular point. The difference as I understand it is whether to include in the filter serialized outpoints for inputs or serialized prev scriptPubkeys for inputs. When hashed these are the same size, and there's an equal number of them (one per input in a block). So the only savings comes from deduping the prev scriptPubkeys with each other and with the scriptPubkeys in the block's outputs. So it comes down entirely to how much address reuse there is on the chain.
 
Monitoring inputs by scriptPubkey vs input-txid also has a massive
advantage for parallel filtering:  You can usually known your pubkeys
well in advance, but if you have to change what you're watching block
 N+1 for based on the txids that paid you in N you can't filter them
in parallel.

Yes, I'll grant that this is a benefit of your suggestion.
 
I think Peter missed Matt's point that you can monitor for a specific
transaction's confirmation by monitoring for any of the outpoints that
transaction contains. Because the txid commits to the outpoints there
shouldn't be any case where the txid is knowable but (an) outpoint is
not.  Removal of the txid and monitoring for any one of the outputs
should be a strict reduction in the false positive rate for a given
filter size (the filter will contain strictly fewer elements and the
client will match for the same (or usually, fewer) number).

I _think_ dropping txids as matt suggests is an obvious win that costs
nothing.  Replacing inputs with scripts as I suggested has some
trade-offs.

I may have interpreted this differently. So wallets need a way to know when the transactions they send get confirmed (for obvious usability reasons and so for automatic fee-bumping). One way is to match the spent outpoints against the filter, which I think of as the standard. Another would be to match the txid of the spending transaction against the first, which only works if the transaction is not malleable. Another would be to match the change output script against the first, assuming the wallet does not reuse change addresses and that the spending transaction does in fact have a change output.

Now lets say these pieces of data, txids, output scripts, and spent outpoints are in three separate filters that a wallet can download separately or choose not to download. The spent outpoint method is the most reliable and has no caviats. It also allows for theft detection as Peter notes, which is a very nice property indeed. If the wallet uses the txid matching though, the txid filter would be smaller because there are fewer txids per block than inputs. So there could be some bandwidth savings to that approach. The change output watching is probably the nicest in some ways because the client needs the output filter anyway. If the transaction has no change output with a unique script, the client could watch for any of the other outputs on the spending tx, but may get more false positives depending on the degree of address reuse.