The surface area of Vault capabilities is much larger than EC2 parameter store and through the lens of our paying customers, most are using Vault for many more of the backends (the most popular probably being PKI).
For pure AWS-based companies, parameter store could provide a fine solution for basic key/value secrets! I don't want to bash at all, I just wanted to make sure for any readers that they don't mistake Vault for purely encrypted K/V.
It's quite frankly not a good experience and really challenging to automate running Vault in a modern environment, all something that is very simple with SSM.
You note this, but I have 2-3 people reaching out to me per week stuck/struggling with vault, who find chamber/SSM and have solved the problem with 1 day of work.
Another would be vendor lock-in. If your code is tied to Amazon, you are then also tied to Amazon, without engineering resources to divorce.
Another reason is, if you are cross-cloud, and not tied to only Amazon.
Also @organsnyder's point in the other comment is also true.
But certainly, if you are married to Amazon, there is nothing wrong with staying married, if it's working out for you and using the EC2 parameter store w/ KMS.
Vault can also work under Amazon just fine, so you can use vault under Amazon, and avoid some of the above reasons.