what makes the PL cursor life-cycle must be in the same transaction?

for example:
begin;
declare cur cursor for select * from t;
insert into t2 values(...);
fetch next cur;
commit;

// after this, I can't fetch cur any more.

My question are:
1. Is this must in principle? or it is easy to implement as this in PG?
2. Any bad thing would happen if I keep the named portal (for the cursor)
available even the transaction is commit, so that I can fetch the cursor
after the transaction is committed?

Thanks