Aside from algae, why is it that bad to have so much light like that?
Plant growth rates are driven by light intensity. The more light, the faster the plants grow. But, they can only grow that fast if they have the needed nutrients to build plant tissue, and carbon is the primary building material. Carbon is supplied in adequate amounts for a high light tank only by CO2. But, the more light you have, the higher the concentration of CO2 in the water you need. If there are no fish or shrimp in the tank getting a high enough CO2 concentration isn't a big deal when you have a pressurized CO2 system. Unfortunately, fish and shrimp can only tolerate a limited amount of CO2 in the water, so with high light you are walking a tightrope between having enough CO2 for the plants, but not too much for the fish.
If the plants don't have enough nutrients to grow as fast as the light is driving them to, they will not be healthy plants. And, the less competitive plants may just give up and die. Unhealthy plants and dying plants are prime real estate for algae colonies to grow on. So, bad algae problems are a primary reason why "too much" light is too much.
Another reason is the increased maintenance required to keep a high light tank healthy. First, the rapid plant growth can quickly create a dense mass of plant matter, which stops water circulation in the tank. But, it is water circulation that brings the nutrients, especially CO2, to the plants. Without good circulation many plants will starve. High light means lots of pruning required - when I had high light I had to prune twice a week.
High light also means keeping the tank, the water and the filter as clean as you can, also to avoid encouraging algae to begin growing. And, it means constantly tinkering with the CO2 system to keep a good level of CO2 in the water even with the constantly changing conditions in the tank. It makes a hobby become a job, something some of us soon tire of. It isn't just plants that grow very fast with high light - algae also grow very fast. You have a much shorter "window of time" to correct conditions that lead to algae starting if you have high light, where with lower light you can wait awhile before having to correct those conditions.
The good news is that "high light demanding plants" really demand good CO2 much more than they demand high light. If you limit the light intensity to 40-50 micromols of PAR, and supply CO2 as if you had high light, you can grow virtually all plants, including HC very well, just slower. And, you don't find yourself tied to a planted tank job instead of a planted tank hobby.