Why rear derailer has limit on front chainring difference?

It is not directly connected to the difference between the front chainrings. Instead, a Rear Derailleur will have a "capacity" which is the total amount of chain it can take up before bottoming out.

The RD also has a value for the small cog (often 11 tooth) and either a maximum-sized cog, or some of the new specs give a maximum and a minimum tooth count for the big cog.

For example, that specs page linked in your question says

Low sprocket_Max. 36T
Low sprocket_Min. 32T
Top sprocket_Max and Min. 11T
Total capacity 43T
Max. front difference 22T

The cassette can "eat up" between 21 and 25 links, and the total capacity of the RD is 43T.

43T less the 21T consumed by the smallest allowed big-cog is 22 T

So your bike might have a 48T big chainring, and the smallest chainring is 26T. Any middle chainring has to be between those.

You could have a 53 tooth big chainring, but your smallest could be no smaller than 31 tooth.

summary The chainring difference is easier to understand for consumers, its just processed the other values.

Putting this another way: Imagine your hardest gear is 48:11 and easiest gearing is 26:32. The rear mech will be almost flat, pointing forward and the chain through will be near straight.

Changing chainrings releases ~22 links of chain, which adds to slack. Your rear mech has to fold up and take up ~22 links, now its in 26:11.

Then changing up the cassette uses 32-11 = 21 links of chain. Thats the lower boundry. If you had a 36T max on the rear, it would use up 36-11 = 25 links of chain. Those two values of 21 and 25 straddle the 22 tooth number quoted in the spec.

Note that Shimano's specs are notoriously conservative too, you can almost always add 2 teeth to any maximum and still have perfectly good performance.

If you had far more difference between your chainrings than 22T, it wouldn't shift very well. 16T is quoted as a reasonable maximum between adjacent chainrings, and 22T would imply a triple crankset with a third chainring.

So if you exceeded the front difference of 22T with (say) 30T, then moving from big chainring to small would release ~30 links of chain, the extra 8 links has to go somewhere. This might let the derailleur rub the chain back on itself in a small-small gearing, or would not put enough tension on the chain resulting in sloppyness and possibly chain slip.

Example: This chain is too long, and is rubbing on itself. The gear is a small:small combo so there is the most "spare" chain outside of the chainrings/cassette.
^{From Is my chain too long?}

There are lots of things in the Shimano specs that are listed that aren't necessarily limits but may simply correspond to their product range.

For example, there is no inherent difference between a 10, 11, or 12-speed MT derailleur, but:

• 10-speed MTB gears when introduced were typically 11-36t cassettes with a front triple chainset such as 40/30/22.
• 11-speed MTB gears when introduced were either 11-46t with a 1x, or 11-42 with 10t front differences. They also launched a longer cage XT/XTR RD which could do 11-40t plus 40/30/22, because they weren't sure if people were going to abandon triples entirely, let alone doubles.
• 12-speed MTB gears are 10-51t but Shimano offer a 10-45t with 10t front difference option as well. These are two different rear derailleurs

Their recent MTB derailleur designs have followed this trajectory:

• Introduction of 'Shadow' RD was around 2007 and refers to the elimination of the top (B) pivot spring, which may make an RD more durable, but makes the rear derailleur less flexible in terms of the sprocket size it is designed for (the preload on a B-sprung derailleur can be adjusted, whereas with no spring this is not possible). Now this system is used on almost all Shimano RDs (Shadow Plus is unrelated to the gear selection and is a clutch system on top of the single spring pivot, so 'Shadow Plus' is not a consideration here)
• The introduction of 11-speed MTB RDs with 2014's M9000 XTR was with a 11-40t triple long cage, and 11-40t double (10t front difference) mid cage RD
• The following year saw the introduction of M8000 XT with an 11-42t option
• The next year saw the introduction of a 11-46t cassette
• The introduction of the 42t then 46t cassettes led to Shimano updating their specs so that both M9000 RDs were ok for an 11-46t 1x system, or a 11-42t double (the RDs didn't changed, what changed was Shimano's cassette availability).
• The updated 10-speed Deore M6000 groupset was released in 2017. Whereas previously the mid cage vs long cage Deore rds were to create a higher total capacity through the use of wider front chainsets, the RD-M6000-GS was in fact nothing more than a repurposed 11-speed rear derailleur, so Shimano specced it for 11-42t cassette with a front double. This is not because it would not shift well with a 11-46t 10-speed cassette, but because Shimano did not yet want to sell such a product, as they would prefer people demanding such products to spend more money, for as long as possible before 'trickling down'.

In other words, the introduction of the single-sprung pivot Shadow system creates two distinct issues within the rear derailleur line-up: 'total capacity', and 'cog size'. Here for example, a RD-M6000-SGS (long cage) is designed for a 11-36t cassette and a 40/30/22 chainset, so the total capacity is 43t. Meanwhile the RD-M6000-GS is designed for 11-42t and a 36/26t or similar, i.e. 41t capacity. That's not a very big difference between 'long' and 'mid', but it reflects more that the latter derailleur will cope well with a large cog.

• 12-speed brought the key change of very large cassettes. Although these are still 'Shadow', Shimano increased their jockey wheel size. For 12-speed you will now find 9/8/7/6100-SGS and 9/8/7120-SGS rear derailleurs (which will be the same design but with differences in the type/grade of materials used). Both are nominally 'long cage', but the difference is that the x120 RD is designed for a 10t-45t cassette and a 10t spaced double, whereas the x100 RD is a 10-51t cassette and a single.

• The 'trickling down' of 51t cassettes to lower priced groupsets means that there is an RD-5100-SGS, which is the same as the RD-M6100-SGS but one is '11-speed' and one is '12-speed' (a purely marketing distinction). Thus you can fit a 11-51t cassette to a HG hub and use any x100-SGS RD.

Here is a video illustrating this:

The author has an existing 11-46t 1x11 drivetrain using the older 11t-jockey '11-speed' RDs (originally specced at 3x40 or 2x40, and upped to 1x46), and fits a '10-45' 2x12 13-t jockey 7120 RD, which shifts perfectly. He then tries a 10-51 1x12 13t-jockey 8100 RD, where the B-screw cannot be adjusted to suit the 11-46t cassette, and it works only very poorly.

So to answer your question:

• cage length determines total capacity, not front gap specifically
• but the lack of a B pivot spring on most modern RDs means that the largest cog size specced for the RD might well represent some kind of limit within which the derailleur can work well (without modifications), so you should pay attention more to 'max sprocket size'
• specs are almost entirely for marketing reasons and there are no technical incompatibilities between many products that Shimano sells but doesn't promote as a set, let alone incompatibilities between products that they don't - they aren't going to test their RDs with Sunrace cassettes and tell you what you can get away with