You cant re-deploy several km's within minutes. Try an hour.
The Tiger 1s engines were limited to 38km/h to improve reliability and if the companies are deployed 3km apart (spread evenly along the front as you suggested) moving this distance will take them 4 minutes and 44 seconds. If grouped in such a way this means that 3 companies (9-12 tanks) can be together theoretically within 5 minutes in optimal terrain, or in more realistic conditions, terrain and speed within 10-15 minutes, however in most situations they will be able to provide mutual support and flanking fire way before that even with some obscuring terrain.
A few heavy tanks are not able to effectively fight a larger amount of medium tanks - that's why people moved away from heavy tanks. A larger number of mediums was better in every way.
All modern tanks have their armor and piercing levels increased from the heavy tanks so I wouldn't say anyone "moved away" from the concept of putting great armor and awesome piercing from big guns, which was the core of the heavy tank.
What nations moved away from after WW2 was producing several different types of tanks since it was not industrially efficient.
All Modern Armor have long barreled high piercing guns of 100-120mm, as heavy armor as possible and weight in at similar weights of what WW2 Heavy Tanks would if not more. ( Compare a M1 Abrams of 60-70 ton or a Leo 2 at 65 ton with a Tiger I at 55 ton for example ).
Many historians argue that the Panther should be classified as a Heavy Tank, or that it was the first prototype of the Main Battle Tank concept ( Powerful gun, Good Armor and Good mobility combined in a single main mass-producable design ). I say it could be considered to be both, and HoI4 agree that main battle tanks can also be unlocked via the Heavy Tank route conceding that they are a merge of the good features of both heavy and medium tanks.
I may be mistaken but as far as I'm aware placing a small handful of STUG's with an entire infantry division didn't cause the Allied infantry divisions to start doing half damage.
No your right, some infantry squads that are advancing against a company of 3-4 STUGs without having appropriate AT weapons would do zero damage instead of just half, and since the advance is blocked none of the other infantry following them through the same route of advance can do much effective damage either but needs to cover, pull back or get mowed down by the MGs or main guns of the STUGs.
Likewise I don't remember reading too much in the history books along the lines of "they were attacked by 2 armored divisions but luckily they had 24 rusty old AT guns and were able to destroy the opposing armor"
Maybe that's because 24 rustly old AT guns have no chance to come anywhere close to piercing proper armor divisions or tanks, neither in reality nor in HoI4? ( And no your 25 Infantry + 1 TD fantasy formations which are on the edge of what can be pierced by obsolete support AT can't be classified as armor divisions ).
Unobstructed, flat terrain with good visibility for 40 km doesn't happen that often (like - almost never). In fact one of the things noted about the tiger was that it very rarely got to use it's range advantage.
Exactly, which is why the 2:1 advantage provided by Armor (50% dmg reduction) is a fine approximation for the averaged tactical advantages provided by superior armor levels, even if it at extreme situations historically could go upwards to 5:1 or even 10:1 Kill ratios of tanks in reality! ( and in other situations would provide a smaller advantage then the 50% in game ).
Historically the optimal Tank divisions in use would have something like 1 Brigade of Tanks, 2 Brigades of mobile infantry and 1 Brigade of SP support (AA/TD/SPGs). But since the highest armor level in the game isn't important enough, this formation is not really that effective in HoI4, with players in competitive situations making divisions closer to 2-3 Bde Tanks, 1 Bde Mobilize Infantry and 0-1 Bde of Self Proelled support. Your suggestion of making it only depend on averaged values would push us even further towards being forced of massing nothing but tanks in the same division to enjoy the advantage, which is totally unhistorical.
For historical combined arms to work properly Tanks need to be able to provide their armor advantage even in divisions which contain alot of infantry and less armored support.