Ok, so it looks like the USPS module (or USPS themselves) no longer allows Parcel Post for local deliveries i.e. deliveries within the same state that the store is located. This is also true for "near by" states.
I’m not sure at what point the Parcel Post (now shown as Standard Post) option is allowed, but I can tell you it is allowed on states that are further away compared to a bordering state. So at some given distance, Standard Post becomes a viable option.
So, I had to enable a second USPS option - Priority Mail. When it comes to same state / “near by” states shipping, the USPS shipping quotes will only allow priority mail.
Now, with out of state shipping, such as California and Florida, the customer will have a choice between Standard Post and Priority Mail 2-Day.