My D applied to 8 schools and she had to write at least 10 unique essays.It was a killer. One of the schools had three extra essays for honors/scholarships that they were very specific and each one in a different format. The other school asked for more creative, personal reflecting questions. In theory I guess one could reuse some essays but my D found that not realistic for the quality of the essays she wanted to produce. That was a surprise to me as originally I thought that you pretty much recycle a couple essays but that was not true. Her common app essay was the easiest for her to write and it was done very early in the process.
Having said all that your kid might be lucky and find more overlap among the schools he chooses to apply. But don’t assume anything before you sit down and look at all the prompts.