That is personally why I like Tidal. Amazing quality, and I can download my playlists/Collections to the phone. I typically do that for the stuff I listen to regularly. Been enjoying their HiFI, and Master quality levels before other services started upping the quality. I have a TON of the services, but honestly Spotify is the one I don't use.
We are a very music driven household, and listen to a large span of stuff.
The services I have -
Apple Music(Part of my One Plan, cause it was cheaper to bundle than to get the things I needed separately) - Lossless is AMAZING, but it takes up A LOT of space on your device if you download it. Quality is there, and with Match can have the stuff you own outside of Apple added to your account. Lossless is as good as Tidal HiFi atleast based on my experience.
Pandora Family(Probably going to Cancel in January - Too many other options currently) - Decent quality, but just not enjoying the interface and it's logic recently.
Amazon Music(Basic is included with Prime - Upgrade to go to HD) - We do the upgrade, and since we have a bunch of Echos it works GREAT. Ask Alexa, and bam. Quality is slightly subpar to Tidal, but still excellent.
Tidal - My favorite. Didn't like the app interface at first, but REALLY like it now. Every now and then, I run in to a song or artist that isn't on it, but they are constantly adding.
As far as Data, most of the above allow download to the device, some with the paid tier. I always recommend that, because well sometimes will be better quality, and obviously like you said, less data usage. If you are downloading, make sure you check your settings to make sure you are downloading at the best quality your subscription allows. It does make a difference. Especially if not connected Bluetooth!
Hope that helps!