I have a more intuitive answer. I have not read all of Tolkien's books but I certainly saw the movies and loved the story. Since I have a long term fascination for exorcism,demonology and theology as well as being into modern science and tech, I think I can give an educated guess of a very good kind.
The primary purpose of any evil objekt is evil and propagation of that quality everywhere. In this regard, take a look at demonic possessions and why evil in its very nature tries to hide itself. Discovery is death for Satan and his minions. Tolkien did understand a thing or two about the nature of evil. If you look at this description of Gollum, and how he degenerates into something horrific over centuries is an analogy and a symbolic reference to evil and it's psychology and constituent. Evil IS ancient. Evil was originally simple, but corrupted by jealousy. I feel pride is stupid, but jealousy was the main reason why his spiritual corruption took an onset. Over time, without the healing element of love and filled with disgust for self-defeat and hurt by being rejected, the corruption became one and whole, with no space for anything holy. It became a distant shadow or its long lost glory and then some.
It understands what is holy and what is good but it itself has lost the ability to transmute itself back.
Now invisibility is important in order to successfully do evil. Human evil is I believe a large part indebted to Satan and his demon army, instigating and acting as a catalyst to our innate bi-natured selves. Remember this is an ancient force we are dealing with.
Tolkien I believe also wanted to also give the analogy of evil being seductive at first with stealth being an inbuilt feature. This also lets anyone who is willing to wear the ring, get an immediate result that entices him to be part of the bad crowd. Remember anything worthy of being good required healthy amount of dedication and work to get at it. Evil tried to make things look easy for quick recruitment so that the benefits seem obvious. It is a ruse.
Without stealth no other feature would survive, so this has to be implicit. For instance, if you make a computer virus with very overt signs with a full blown application saying that "this is a computer virus-will destroy your computer" with a GUI dialog (and is not a joke application), I am sure only the mentally retarded would enable the whole application and execute it purposefully. Rootkits especially make use of memory address overwriting of essential system function address tables to intercept function calls and do their bidding without the user knowing about the presence.
God (or Good) has many faces (quite overt and visible), Evil has no known face as such -just different appearances. The difference is huge. A set of masks do not portray anything but deception. Which is also one of the primary methods of how evil functions. Seeing the Devil can scar you for life as the damage is spiritual and needs solid support of the good energy if you have to survive the attack. Judging from accounts of priests and Christian writers worldwide, and in my own experience with demons (not as victim :)) as well - evil cannot enter into a potential host in a normal way. It has to prepare a ruse developed with careful study and deploy selected personnel assigned to that particular target person or thing. Thus, building confusion and deception as well as tried and tested methods like "the broken record technique", scare tactics etc. are just the means to an end. The main objective of evil , mankind's destruction in mind, body and spirit of every individual. It is our primary enemy.
Evil also has a tendency to trap victims by debating for them of the side they should take by taking advantage of hurt feelings or potentially recoverable situations and turning gold to lead. However, when the time comes, evil will rebuke you for being such a fool and believing it (no gender here) and not surprisingly will try to break you by holding you accountable for being so gullible. It takes immense pleasure in deceiving its victims. Explicit appearances and scare tactics are only required when the usual stealthy mode of combat does not work good enough and more deterrence is necessary. This also means that the evil enemy has failed its initial and primary attempt. To expose itself and make itself known is the last thing evil wants.
The alternate dimension where the wearer of the ring displaces to, is quite similar to the preternatural realm of the demonic kingdom. Where right at the 4D (time and space) - Cartesian co-ordinate of your current location, another dimension parallel to it exists like a second plane of energy band in atoms. It is visible only when certain criteria is fulfilled, just like electrons leave or enter a specific energy band in an atom around the nucleus. According to recorded and interpreted interviews of demons in possessed victims, they say that the number of demons banished to earth is so large that if they took physical form they will cover the sun and earth would be starved of its light.
In terms of computer architecture, the concept of privilege rings look quite resolute. The kernel or core of the system wants to protect itself from external application based communication parameters so that it can run as smoothly as possible. This abstraction runs in a protected mode supported by the microprocessor, where in user mode or regular application processes do not interfere with the core functionality of the operating system. However, kernel mode communication can be availed of and made use of with the special programming interfaces (APIs) and toolkits, like device driver programming.Computer exploits and hacks done by malware and malicious code, exposes this kind of devious thinking wherein a feature loophole or a substandard design can be taken advantage of and used to infect the machine, inspite of existing guards in place. Thus security is a full time job, which requires just one hit to prove that it needs to be better. The evil side requires just one hit to do the real damage and run away after that. Less to lose more to gain. For the good side, its everything to lose and everything to gain by not being careful and by being careful.
You could also read books by MD Scott Peck and Eric Fromm to understand about the evil psychology. Crimimal science books also do a good amount of description and demonic possession and exorcism as subjects are like drinking from the fountain itself. Further, computer security is also very related as it is people who are developing this stuff and it is a by product of human intelligence.
I believe, Tolkien portrayed evil in very good light with solid symbolic significance.