Simplicity is a shortcut to correctness. Let's Encrypt is a simple thing to implement. Relatively speaking of course. It would be tempting (unbearably so for a for-profit issuer) to have manual issuance, this means at least duplicating the effort as every system can also be manual and must have the appropriate checks in place for that.

As an example of how wedded Let's Encrypt is to simplicity, part of routine application process is to show your certificates expire properly, often a CA would manually create a certificate which either was already expired (back dating it but arguably this is allowed for technical procedures) or had a very short lifetime and so would expire by the time the trust programme examines the demo cert. Let's Encrypt instead issued an ordinary 90 day certificate, using the same automatic process as their subscribers - and then just waited months for it to expire. Like a boss.