I understand how shields would be too heavy for one man, but why didn't they use some that multiple men could carry to protect themselves in small groups?
Some kind of two person wide barrier that 4 or 5 men could crouch behind where they could carry them up over the trenches for at least temporary protection.
During WWII, the Soviets experimented with metal breastplates that covered only the vital organs. In order to protect from rifle bullets at reasonable ranges, the breastplate had to be so thick and heavy that the soldier wearing it tired quickly. The breastplates that were issued in large numbers were much thinner and provided reliable protection only from pistols and SMGs, which were a rarity in WWI.
A barrier big enough to completely cover 4 or 5 men would be much larger than 4 or 5 breastplates, and therefore much heavier. The form factor would mean that it would be much less convenient to carry, since the weight would have to be supported with the arms rather than the entire body.
A solution similar to what you're proposing eventually came about: the armoured sled. A tank would drag an armoured box full of infantry into battle, sort of like a winter-only budget APC.
So anything big enough to provide the protection would be extremely slow and heavy. It might be ok for the first few feet out of the trenches, but as soon as they got any significant distance into no mans land the wires, obstacles, and terrain would make movement difficult to impossible, and the grenades and artillery would kill the soldiers before they could slowly make it to the trench. Trench warfare was known as static warfare, not static as in there was no movement, but static being a military term used to describe positions that were long term enough to allow heavy equipment and artillery emplacement that would be impossible during "maneuver" warfare. Since guns could be emplaced and already had the range and angle set, artillery could be called to repel an attack rapidly. So by the time the shield started trying to cut their way into the fortifications they would already be taking shells. Here is a section from the British trench warfare manual emplacing the importance of speed.
Arrangements have been made by a carefully thought out system of intercommunication for the maximum cooperation between artillery and infantry, both in attack and defense, and artillery has had time to register on all targets within range. Thus either side has it in its power to concentrate heavy fire at very short notice upon any selected target, and to maintain that fire for a length of time which difficulties of ammunition supply would put out of the question in maneuver operations. Consequently, the rapidity with which artillery can form a barrage to meet attack makes it necessary that the moment of the assault should come as a surprise, and the trenches from which an attack is to be made should therefore be within close assaulting distance of the opposing front line.
Then, even assuming that they were able to cross the entrenchments and approach the first line of trenches, the whole trench would be specifically designed to kill things in multiple angles, called oblique and enfilade fields of fire, which means that multiple gun emplacements should be able to target any single point on the battlefield with fire from multiple angles, rendering cover from any one direction useless. From the same British manual:
A consideration of the above shows that there are certain features which are essential in a system of trenches. They must be strong, to resist heavy bombardment; they must be sited and designed to favor, by the utilization of oblique and enfilade fire of rifles and, above all, of machine guns, the development of the maximum volume of fire over any part of their front; they must be protected by a strong and well-hidden wire entanglement, in order to retain attacking infantry under this fire;
These are the reasons that fast tactics, close ranges, and surprise attacks were the name of the game. If you linger in no mans land you will die. It is better to rush quickly past the kill zone and risk a bullet, then to block bullets and almost surely die to artillery, grenades, and fire from adjacent positions.