So, basically, as long as you hold/receive/send the tokens without converting them to sats, you don't affect channel liquidity and this can be done when the recipient is not online; however, this comes with centralization and counterparty risk. For me, this is a hefty tradeoff. Besides, as I recall, the main advertized utility of these token was privacy, now it has moved away from this.

Also, coming back to having an ability to receive sats when offline, I recall Supertestnet proposed #hedgehog protocol that could be a solution to this problem while not requiring centralized mints and counterparty risk.