Quote from: miner2251 on June 29, 2021, 06:10:17 PM

miners collect transactions and try to find some value that can be added to "r" and can lead to smaller signatures.

The hardware the miners have (ie. ASIC) is designed to compute one thing and one thing only. That is to compute double SHA256 of block headers. To compute EC operations you'll need to use regular hardware (CPU/GPU) or a different specialized hardware (a different type of ASIC) to make those computations.

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Assuming one satoshi per byte fee rate and 2,000 transactions in the whole block, saving 5 bytes per transaction would mean earning 10k satoshi per block

Fees are paid per byte not per transaction. If a block contains 1x 200 byte transaction paying 1 sat/byte the miner makes 200 satoshi and if it contains 2x 100 byte transaction each paying 1 sat/byte the miner still makes 200 satoshi.

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So, even if Segwit signatures are outside of the block,

SegWit signatures are NOT outside of a block. They contribute 1x to the total weight while everything else is 4x.

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Unfortunately, that kind of service cannot be applied for taproot, because that signatures has fixed size of 64 bytes, but they are compressed to single signatures anyway, so there is less need for that kind of compression.

The main reason why Schnorr signatures are smaller is not because they are "compressed to a single signature" it is because we got rid of a lot of overhead with DER (8 bytes to be precise + 1 byte from pubkey). If you try to make r and s lengths variable you'll have to re-introduce DER (or a similar variable length encoding) which will add the overhead again.