Should I use Cognito Identity Pool OIDC JWT Connect Tokens in the AWS API Gateway?

I noticed this question from 4 years ago: https://repost.aws/questions/QUjjIB-M4VT4WfOnqwik0l0w/verify-open-id-connect-token-generated-by-cognito-identity-pool

So I was curious and I looked at the JWT token being returned from the Cognito Identity Pool. Its aud field was my identity pool id and its iss field was "https://cognito-identity.amazonaws.com", and it turns out that you can see the oidc config at "https://cognito-identity.amazonaws.com/.well-known/openid-configuration" and grab the public keys at "https://cognito-identity.amazonaws.com/.well-known/jwks_uri".

Since I have access to the keys, that means I can freely validate OIDC tokens produced by the Cognito Identity Pool. Moreso, I should be also able to pass them into an API Gateway with a JWT authorizer. This would allow me to effectively gate my API Gateway behind a Cognito Identity Pool without any extra lambda authorizers or needing IAM Authentication.

Use Case: I want to create a serverless lambda app that's blocked behind some SAML authentication using Okta. Okta does not allow you to use their JWT authorizer without purchasing extra add-ons for some reason. I could use IAM Authentication onto the gateway instead but I'm afraid of losing formation such as the user's id, group, name, email, etc. Using the JWT directly preserves this information and passes it to the lambda.

Is this a valid approach? Is there something I'm missing? Or is there a better way? Does the IAM method preserve user attributes...?