You would never, ever, drive a tank the entire distance from the factory to the front line. Unless the front line is 10 miles away from the factory, but then you’ve got a different problem altogether: you’re losing the war.

Since you ask about German tanks in the body of your post, I’ll focus on German tanks. You are correct that driving a long distance at full speed would cause problems to the tank’s mechanism, problems which would only become more and more serious as you covered more ground. The way to deliver tanks across long distances was mainly by train or, depending on the point of origin and destination, by ship (in the case of the Wehrmacht ships would be used for resupplying their forces in Africa). Regardless of whether you’re looking at a brand new tank or an overhauled vehicle in a repair yard, it is, therefore, advisable that there be a railway facility near the point of origin.

Robert Kershaw in his ‘It Never Snows In September’ provides the following description of how Panzerkampfwagen VIB Tiger II tanks would be entrained for transport to the Netherlands, to participate in repelling the Allied landings of Op. Market-Garden. The scene takes place on 21 September 1944 in Ohrdruf, which is about 390 km away from Zevenaar (where the train would terminate its journey) in a straight line.

Forty-five factory-new 68-ton Porsche ‘Tiger’ IIB tanks were carefully coaxed and swivelled from loading ramps on to the flat rail cars. . . . Chains rattled through retaining rings and wedges were hammered home as crews secured their valuable charges for the rail journey to the front. By midnight the steam locomotive, cascading steam and blowing sparks into the air, had puffed vigorously out of the siding on to the main line. Crews made themselves comfortable as best they could in the few personnel carriages made available. It would be a long journey. . . . Schwere Panzer Abteilung – Heavy Tank Battalion – 506 was supposed to arrive in the Arnhem area by the early morning of 24 September. . . . They were bound for Oosterbeek and Elst.

Note that it took about 2 days for the train to cover a distance which today could be covered in four hours, easily, and in less than two hours by some trains. This was mainly due to Allied air superiority which allowed Allied fighter bombers to attack trains almost at will.

Then, once in Zevenaar and Elten, the time came for the tanks to get back on the ground:

Clanking and thumping, the rail flat cars came to a final squeaking halt in the railway siding . . . during the night of 23–24 September. Climbing over dimly-lit hulls, panzer crews began removing foliage and camouflage netting. Following a harsh whirr, Porsche engines burst into throaty, smoky life. The complicated task of unloading the 60-ton steel Tiger IIs across ramps began and continued throughout the night hours; whirring chains clattered through rings and wedges were knocked loose. . . By early morning on 24 September Major Lange’s 45 [tanks] were marshalled into columns, and noisily and jerkily set off towards their various forming-up points. Two companies – 30 tanks in all – were despatched to the 10SS in the Elst area, where they leaguered up in a small wood three kilometres north of Elten. The remaining ‘Hummel’ heavy assault company of 15 Tiger IIs was sent to the 9SS in Oosterbeek.

So, as you see, tanks would be expected to cover only a short distance on their own. In this case it was about 15 km. The smaller the distance, the better (you save fuel, avoid malfunctions etc.), but also you wouldn’t want to bring the tanks too close, close enough for the enemy to bring their anti-tank guns to bear on the virtually immobile and defenseless vehicles.

The central problems with the perspective presented have already been addressed so I'm just trying to add a bit that might help with understanding how to think of the maximum speed of tanks. If you consider your average North American car, the odds are the maximum speed is probably around 80-90mph. Even discounting law enforcement, when can you ever really 'max-out' the speed of a car? Certainly not in cities or rush hour highway traffic. Tanks are basically in the same position in pure speed terms.

Tanks also operate as part of a group in general. It isn't just you going from A to B but 10-20 people all going in their own cars. To get some sense of what is faced, imagine a funeral procession with everybody needing to leave at the same time and arrive at the same time. That is what tanks have to do as a routine.

Finally, already touched on, are the pure logistical problems associated with moving any distance (because tanks operate as part of a bigger unit with all sorts of other vehicles, not to mention the technical issues). When you put it all together, the technically maximum speed you find on pages like mine are a lot like the ones you find on a car's speedometer. A classic work on this subject is van Crevald's Supplying War.