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Capacity is the issue here, and Muun is not self custody. Even if you use a self custody wallet like Phoenix or Brezz or Zeus running your own LN node and Electrum server, you are limited to few hundred dollars.
I think $1000USD+ is totally possible on LN these days. You are only swapping in and out so no real risk from the Lightning providers. Is that not enough capacity? A much easier experience than trying to fuff around with a Coin Join IMO.
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$1000+, It will always depends with which LN nodes you are interacting, most will still have a cap around the $500 mark, but that is already an improvement, early 2022 was circa $300, is moving higher. You may have a channel with a $1000+ capacity (rare since you don't want to HOLD what you don't want to spend in a LN wallet and therefore you won't have large channels opened, nor the other parties unless there is constant usage) but the receiver most probably won't.
Paying for goods and services like a new car, an ASIC miner or a major repair at home with LN is currently not possible since it will be above the most common channel capacity, therefore we will end using on chain payments, that is where privacy is needed and we do not have it. If the buyer doesn't know what is doing will end up giving away the historic of all his/her transactions and the balance in the used wallet.
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