Yes, but you can't do it trustlessly not even with all the crypto black magic in the world. Otherwise it would be great. People in Bitcoin space have been tryi

Yes, but you can't do it trustlessly not even with all the crypto black magic in the world. Otherwise it would be great. People in Bitcoin space have been trying all possible off-chain payment solution they could think of. "Sidechains" are a concept similar to your thing where people deposit bitcoins, however they seem to be impossible to do on top of Bitcoin (and on top of Ethereum too, even though people there have all computation tricks in the world at their disposal). In the Ethereum space people came up with something called "Plasma" that is supposed to solve this and allow a big number of off-chain system use-cases, but it has an insurmountable number of flaws when you look closer. In the Bitcoin space, there's an idea for implementing sidechains in a trust-minimized way (not 100% secure, but relying on the same game-incentives the power Bitcoin itself) called "Drivechain". Most of the discussion you'll find about "sidechains" on the internet is either people pitching the drivechain solution or criticizing or ignoring it completely and talking about Liquid, an off-chain payment system managed by Blockstream that is not trustless nor has any game-incentives.