I think I know what is happening- and, if so, your ‘overload’ metaphor is closer than you think. I have personal experience with Tidal and the Modi 2 and the Modi Multibit. But IME the problem isn’t the DAC.
Assuming you are using the Tidal app on a computer (I use a Mac but that is not important to what follows), open the app and look at the volume control setting within the Tidal app.
If it is all the way up (to the right), which is the default, there is your problem. You might (as I did) assume that full volume on a digital slider would provide unity gain (one of my player apps actually states this), but you’d be wrong. The Tidal app (along with many other audio apps) actually applies gain at maximum volume setting, whic results in clipping on loud passages. I discovered this after installing SoundSource on my Mac. This app has small meters that change color when the signal clips. Clipping is bad and will sound bad, and you will notice immediately once it is gone. If the audio is clipping, there is indeed no benefit to the ‘hi-fi’ upgrade.
Fortunately this problem isn’t that hard to fix- its just that nobody seems to know about it. For those who use a Mac, buy Rogue Amoeba Sound Source ($20). Play an album with really loud peaks (Chick Corea’s Trilogy works well) (another good candidate would be the infamous Telarc 1812 cannons) and adjust the volume down until the meters stop turning red on the loudest passages. This will actually be about 2/3 of the way up on the slider. NOTE, selecting the DAC as the output device grays out the System volume adjustment so you must set the source app correctly. Reducing the volume downstream doesn't 'un-clip' a clipped source. Since it is a question of levels and not bitrates, downgrading the bitrate wouldn't fix the problem either.
If you use a Windows machine, you’ll need to do a little research to find the appropriate software to accomplish the same thing. What you need is probably a VST metering plugin that incorporates some type of clipping indicator. You need it to sample the output of the player or streamer app directly. I'm sure there is something on the Windows platform that does something similar to soundSource or AudioHijack. Set the meter to 'Peak' mode and experiment as described above.
I have found that virtually all digital music apps with their own volume controls have this problem - both streamers and players. Only VLC has a little tick mark on their volume slider denoting unity gain. On a player app, you can also play a calibrated test tone through a metering plugin to accomplish calibration. Streaming apps are a little more challenging to set.
I think you’ll find, as I did, that a signal that isn’t clipping sounds better than one that is, and that once the real problem is solved, the hi-fi stream will reveal itself as a worthwhile improvement on quality recordings. My Modi Multibit sounded like a whole different animal after getting things right. Garbage in, garbage out.
I wonder how much business the lossless streaming services are losing due to people not actually getting the SQ they’re paying for. Clipping by definition isn't 'lossless'. I see debates about which streaming service does the best job delivering the exact same digital file to your DAC. I also wonder how much money gets spent on faulty solutions. This problem came up in another thread, and the OP was inundated with suggestions about which magic USB cable to buy. Solving the clipping will be much more effective at lower cost. Ever hear someone say that digital in general (or streaming in particular), sounds ‘hard’? I wonder if this could be why in some cases?