Would love to hear a more detailed answer too, but I would like to offer some preliminary takes on the question:

While it is true that tanks were originally used to lead troops safely across No Man's Land, we should bear in mind that that was not the sole purpose underlying its conception, nor is that purpose very well fulfilled by merely having a big metal shield with wheels.

No Man's Land was not simply an empty expanse--it would have been full of complex and deep trench networks, thick rows of barbed wire, craters made by exploding artillery shells, rubble and so on. Soldiers burdened with the weight of their own personal equipment in addition to a huge metal shield would find such terrain near impossible to traverse. A key reason why tanks are outfitted with caterpillar tracks instead of big wheels (besides the physics of having to support a very heavy mass) is because the significantly larger surface area enables them to cross the thick, immobilising mud of the battlefield with less difficulty. Wheels are much more likely to get stuck in the mud and troops would probably find themselves in the heat of enemy fire trying to dislodge their shields.

Tanks also served other important purposes, such as destroying an enemy's hardened defensive positions at range (such as bunkers, pillboxes, machine gun nests, barricades or other battlefield obstacles) or crushing through barbed wire with its massive tracks in preparation for a more general infantry attack. Having a large motorised platform would allow armies to equip the kind of heavy armaments required to perform this task, for example large calibre guns like the 6 pounder cannons on the British Mark V that ordinary infantry men would not be able to carry or move around easily. Interestingly, many guns of similar calibre were in fact mounted on unmotorized wheels with a metal sheet in the front as some form of rudimentary armour--very similar to the shield idea you brought up--field artillery. The battlefield effectiveness of such weapons were often unreliable since difficulties encountered in moving the artillery guns around by manual pushing and relying on wheels hindered their ability to provide quick and decisive direct fire support.

Finally, troops did not always follow behind a tank that closely. Early tanks were, after all, rather slow. Realistically, tanks would have been used, in theory, to attack first and breach enemy defensive positions, followed by an infantry attack to exploit said breaches. The heavy armour placed on tanks was intended to protect the crew and its armaments from the shrapnel and bulletfire they would encounter while pressing on towards enemy lines. The armour is plated on all sides because artillery can land behind an advance, causing damage to the rear (another reason why a unidirectional shield would be ineffective), but the resulting mass necessitates a sturdy, motorised chassis with enough horsepower to keep moving.

Hope this gives you some food for thought!

Edit: typos