I do concurrent requests just fine and they have no noticeable performance impact. Not all local hardware is equal. Also, humans have to sleep. Agents don't, so processing stuff over night and reviewing in the morning just gets more utilization out of what is already there.
With cloud agents I also process stuff overnight. But my gpu is limited. If I want to OCR a high number of documents or vectorize data, I can't run an LLM at the same time. I use remote models and use my compute for running commands on my desktop machine.