I understand your question about horizontal motion. One thing you have to be aware of is that you don't want any significant horizontal motion as is obvious if you have had skipping due to wobbly floors. Also horizontal motion will likely have a greater effect on platter rotation as it will be inline with the belt moving the platter. The suspension is basically designed to quickly change horizontal motion into vertical which is less likely to disturb the motion of the important parts.
It is true that the suspension is also designed to separate the platter/sub chassis/arm/cartridge from the motor. This was especially important in the days when the LP12 was designed, as motor vibration was a significantly bigger problem then as opposed to now. However, there is still some small amount of motor noise that needs to be dealt with or you would be able to strap the motor to the sub chassis.
I don't agree with the idea that the softer mounting of the Radikal 2 motor, or of the Lingo 4 for that matter, is the solution, nor that it is the biggest part of the improvements of these units. You will notice that the Majik LP12 still uses the very rigid mounting for the motor that has been used for decades - there has been no change to a softer mounting. What most probably don't know is that in the very early years there was a more compliant mounting using a thin piece of cork. Linn found that the more rigid mounting improved the performance substantially. They even converted the dome shaped washers used from aluminum to stainless steel quite a few years back for an even more solid connection. The type and amount of damping used in the motor mounts of the Radikal 2 and Lingo 4 are completely different, as they both are from the solid mounting of the Majik motor. I am pretty sure that each motor has a unique noise spectrum and level and the mounting systems for each is designed to deal with that vibration in the optimal manner. The vibration spectrum of the DC motor in the Radikal is quite a bit different from that of the 12 Volt AC Lingo 4 motor driven by the FPDA created waveforms which are also quite different from the vibrations of a 120/240Volt AC motor driven by the AC waveform or the waveform created by the Valhalla or Lingo 1 through 3. Mounting the motor completely separately may allow for more motion between the motor and the bearing/platter which is also not a good idea.
Now on to the connection of the items inside the loop. Yes they are made of different materials but Linn has gone to great lengths to make those materials all work together. They are all very complimentary. Also Linn is very strong on using the there point connection to assure the rigidity of the connections and eliminate unwanted motions. This is obvious in some places and less so on others. The cartridges from the Krystal on up are all three point mount designs as was the Troika, the first of this type. All of them from the Troika on have had aluminum bodies. All of them have raised lands so that the top of the cartridge only contacts the headshell at three, high-pressure points. In the Ekstatik and the Kendo the material of these raised lands has been changed for the first time to a bronze/aluminum alloy that Linn states allows for an even better interface of the cartridge with the headshell. Note also that all Linn headshells are aluminum, with the Ekos SE/1 machined from solid billet (possibly the Arko as well but I'm not sure). But that is just one interface. All Linn arms (as opposed to those like the ProJect 9CC, Jelco SA250 Linn and Krane used on versions of the Majik LP12) have a three point contact of the arm pillar with the mounting collar. There is a cutout opposite the set screw such that the arm tube is pressed against two edges by the third point of the set screw. This has been the case ever since the Ittok LVII, Linn's first arm. The Keel is also designed so that the bearing housing contacts it at three points as there are three lands on the underside machined out of the aluminum that the top of the bearing housing presses against. This is something that I have not seen on any of the third party copies. Those are just the visible ones. But I was told by a Linn tech person that it continues inside the Ekos SE/1 (probably the Arko as well) where a three point attachment is used on some of the parts. I haven't seen one taken apart so I can't say where but the headshell to the arm tube and the arm tube to the bearing structure are two likely points.
All of these rigid connections, and the materials used in the construction of the parts, are there to help assure that acoustical energy that hits the cartridge/arm also hits the platter/bearing and sub chassis in the same way so as to nullify as much as possible a differential movement between the arm/cartridge body and the platter/mat/record that would interfere with the ability of the stylus to extract the maximum of music from the groove. Of course there are compromises involved in all of this, just as there are in anything in the physical world. Also obviously you can't have a suspension that is perfect hence the fact that things like top plate materials, plinth materials and the stand you put the LP12 on do all have an effect on the musical reproduction.
But it is in knowing which compromises cause the least musical harm that the brilliance of the LP12 design shines through. That Linn has managed those compromises very well and balanced the designs of the various parts expertly is to me proved by the tremendous amount of musical enjoyment I am able to extract from my records with my Klimax LP12. It is further proved by the impressive list of upgrades to every part over the years, with almost all of them being actual musical improvements over previous models. (I know there will be some contention here and there as to whether parts like the original Arkiv was better than the beloved Troika for instance, but such minor things aside it is still quite an enviable record.) It is also indicated by the fact that I have yet to hear a third party component for the LP12 itself (leaving out arms and cartridges) that I felt was an improvement over the ones Linn made with two exceptions: the Rubikon sub chassis which was musically between the Cirkus version and the Keel but was later outperformed by the Kore for less money, and many of the custom LP12 plinths that Chris Harban of Woodsong Audio used to build (and sadly no longer does).
Bringing the arms and cartridges back into the conversation, while I have heard other arms and cartridges I felt sounded good on the LP12, a number of which I have customers using on their LP12s (some that come to mind are Koetsu, Ortofon, Grado, Lyra, AT, Dynavector, Naim Aro, Grace 707, Breuer, among others), I have not heard any I would own over an Ekos 2 or Ekos SE/1 in terms of arms and over an Akiva, Kandid or Ekstatik in cartridges (or even a Troika when you could get them). There is a synergy between Linn arms and cartridges (as there obviously is between Linn arms and the LP12) that even other cartridge makers have alluded to. But if you prefer the flavors of other cartridges you can certainly get stunning perfromance from a Koetsu. Lyra, Dynavector, Ortofon Cadenza, etc. in an Ekos SE/1 or an Ekos 2.
Hopefully this answers some of your questions.