Lambda and Parameter Store

I guess this is more a suggestion than a question, but I'd love to hear the opinion of other users. Using layers we can integrate Parameter Store (or Secret Manager) with lambda, which is extremely useful since values are cached etc. However, I was thinking, wouldn't it be more efficient to simply "push" values from Parameter Store to lambda metadata (i.e. to env variables, which anyways are encrypted at rest)? In that way we could control everything centrally from Secret Manager, no need for lambda extensions : Parameter store would keep a list of "subscribed" lambda functions and propagate changes whenever they occur, information would be then retrieved locally from the lambda function, no API calls, etc.