so, the whole thing is just marketing gimmick after all
Not at all. But mr nctnico do not know how these work and what is what.
First do not mix persistence. It is only somehow part of this thing.
Important part of intensity gradation comes from data density on screen what produce part of intensity information.
Persitence tell how long time data stay visible after real data disappear (simplified)
Intensity is produced from amount of data affecting one area of display and this is important part of intenmsity gratadion what also is some times hard part to many manufacturers but also it need hardware suitable for this.
There is three "dimension". X, Y and Z
Without intensity gradation there is just X Y and Z is 1 or 0
With intensity gradation Z can show also other values than just pixel on or off.
Today oscilloscopes can work much faster than older digital scopes and they have enormous amount more data processing brute force.
TFT screen is updated perhaps example 25 times in second. One updated TFT image may have hundreds or even thousends of horizontal sweeps stacked over each others, Now if think display pixels. Theree is perhaps one pixel where signal have "visited" only once and then there is some pixel where signal have visited many times in this one display frame what include lot of horizontal sweeps aka waveforms. Some pixels have visited more times than others and this is part of building brightness information. Other part is one individual horizonatl sweep. Also this one have more or less density in these cases when displayed waveform data length on the screen have more samples than display width. Example if in some scope display waveform length is 700 display pixel in dislay but it have 700000 data points. Now every horizontal one pixel wide vertical column have 100 dataq poits. But signal may include noise and signal vertically so these 100 pixels are plotted to screen to this column. Now, some pixels may have several data points and some pixel less and also this density affects brightness. After next 1/25 s new TFT frame and all same happen again and now, just from begining. Our eyes do not normally so much note this due to this frame interval.
But then... then there come other important part. Persistence.
Without persistence there comes new TFT frames (what include more or less these overlayed waveforms (in think analog scope, many horizontal sweeps and this inside one frame build intensity)
After this 1/25s there come new TFT frame without waveform data from previous TFT frame if there is not any persistence. Peresistence is other and very important. Without persistence if there is one waveform what have anomaly and then several where signal is repeating steady you see this anomaly only one TFT frame time. Just perhaps your eyes can note it if you tightly watch screen without blinking eyes.
So this intensity gradation nicely tell some information about data distribution (example signal have some random noise, then trace is fat but intensity is center weighted) but all is only in one TFT frame and after then there come new frame what overwrite all old. Exept if we have persistence. With persistence part of previous frame data is also copied to new frame... simplified: If persitrence time is 10 second and there come one anomaly and all other waveforms in all frames are equal... next 10 second you see all these refresshed frames and it also keep visible this one anomaly until 10s tmer is full and it disappear.
Intensity gradation is much more than just persistence. It not anly how old is some data point but also how dense they exist on the screen. We can think it is data density tranfer to Z axis aka brightness.
Experienced use can use of course both these things... but example for glich hunting persistence is perhaps most important - exept if oscilloscope can regognize anomalies and with its own intelligency detect these and show to us.
Data density related intensity is also useful in many cases. Which one is more or less important to individual user in many different cases, these are differently weighted by user and case what he is doing.
Perhaps I can live without intensity gradation but without adjustable persistence not. Even in analog scopes era I have adjustable persistence and screen memory when need. Problem was mostly that phosphor is more os less slow...even microchannelcrt is slow if compare today digitals.
We need phosphor like intensity (but not full emulation) + adjustable persistence (and nice if it also have time related intensity change but this is very different thing than previously told density related brightness gradation.