Meanwhile, Phoenix doesn't show a channel being opened, it shortly showed a new channel as "closed", but that one disappeared. On-chain I can see my transaction is split up into several other transactions already, each with 12 sat/vbyte fee (which is still more than the total fee ACINQ took from my deposit). This was the largest deposit I've sent into LN so far, and channel opening is custodial. I don't know if a channel was opened for me, but if it's with 12 sat/vbyte, it's going to take a while.
Update: I have an open channel! It was opened (with 13 sat/vbyte) a few hours after my deposit confirmed, and a couple hours later the channel and balance became available to me. Here's the interesting part: The on-chain transaction opening the channel isn't confirmed yet! As far as I know, that's not even possible 
So, and I'm slightly speculating here, this would mean ACINQ accepts LN-funds coming out of a LN-channel that's not confirmed on-chain yet. Because they're the ones who opened the channel, they can be sure it's not going to be double spent at some point and will confirm eventually. And I also expect their own hub to have confirmed channels with third parties, so third parties aren't dealing with an unconfirmed channel. So far so good, I am quite happy I don't have to wait (weeks?) for this transaction to confirm. But I'm not sure if this means the channel is now more or less custodial: if I try to close the channel, the opening transaction still has to confirm.
Update (6 days later): the transaction that opened my LN channel got confirmed. All this time I've been using Phoenix Wallet without problems.
If this is true, there is no risk to ACINQ because your "deposit" has already confirmed. Allowing a LN transaction to be processed when the opening transaction is unconfirmed is opening up risk to the counterparty to the channel only, and no one else in the LN network. This is probably a setting that should be set to "disable" by default though.