My limited knowledge tells me that BTC will lose its main reason for existence - solution of Byzantine generals problem, allowing trustless store of value. With what I've read about SegWit, it's a practical solution to improve transaction throughput by moving transactions off blockchain, which in turn removes trustlessness from the equation. I'd like to know if my conclusion is correct.

Segwit enables many things, one of them is Lightning Network. While that is an off-chain transaction system, it still is trustless and decentralized.

In fact the transaction cost reduction could make custodial services like exchanges less attractive and improve decentralization.

> With what I've read about SegWit, it's a practical solution to improve transaction throughput by moving transactions off blockchain

SegWit has nothing to do with this — maybe you are thinking of Lightning Network?

Possibly. I guess I need to study it a bit more in depth, usual grad-level crypto & distributed algorithms aren't sufficient.

Why would they be? SegWit is a specific application you of course would have to read about to understand.

1) Segwit does improve transaction throughput, but it does so by improving the efficiency of transaction storage on the blockchain.

2) The Lightning Network improves transaction throughput by moving transactions off the blockchain, and requires segwit to be active for reasons apart from its transaction efficiency, specifically that it fixes the transaction malleability problem.

1. Actually that is incorrect. SegWit transactions are several bytes larger than old style transactions.

I think that's off-chain networks like Lightning, not segwit

Lightning is trustless and decentralized

You have been misinformed. SegWit does not move anything off the blockchain. It just rearranges things within the blocks.