Heat input is an important factor to consider for a few reasons. It can affect material strength, corrosion or chemical resistance, and cause excessive distortion just to name a few.
When a welding procedure is developed, typically there is a min/max preheat or interpass temperature required. When welding on thicker sections of metal, it acts as a heatsink, therefore "quenching" the weld, which can cause internal cracking, that is why preheating is often required prior to welding and interpass temperature be maintained.
Metals with higher carbon content often times require preheat (typically) because the the grain structure in the material doesn't expand and contract as evenly as other materials, and thus can crack if cooled too rapidly.
Aluminum can be affected by excessive heat input. If it stays at high temperature for too long, the strength of the material is considerably compromised. Often times, there will be a limited amount of times an aluminum weld joint can be repaired.
Stainless steels are extremely sensitive to excessive heat. If proper care isn't taken, SST can lose it's chemical and/or corrosion resistance as the metal becomes sensitized.
Heat input isn't just about adjusting settings on the machine. Factors such as the welding process, joint fit up, groove angles, welding position, contribute to heat input.
Example; if you have a procedure for welding a single V groove joint, with a 60° included angle, 1/16 root opening, with the GMAW process, and someone decides to change the groove angle to 90° with 1/8 root opening, and uses the GTAW welding process. You will now be adding considerable more heat into the base metal. The 90° groove angle will now need more filler metal, as will the 1/8 root opening, which will likely require slower welding travel speeds and/or more passes to fill the groove all of which has the potential to drastically change the metallurgy. These affects can weaken the base metal and or weld joint resulting in a failure.
Remember, when a welding procedure is established, basically a "recipe" has been created to weld material "A" to material "B" using a given process and set of variables. When the variables are changed beyond the limits of the given welding code, there are many things that affect that recipe, and heat input is one of them. If someone has developed a procedure, and gone through the trouble of adding restrictions on heat input, there's probably a good reason for it.
Hope this helps.