You are correct that ERA’s may bounce around; that just really depends on the payer and which clearinghouses they will allow to send to them. Some payers only accept claims from one clearinghouse.
Now on to your question if you’re allowed to get the era’s directly, and again that depends on the payer but the answer is probably yes. But you would have to go to every portal of all your payers and download all the era’s that way.
I’ve found most government payers allow for direct connection, so as for me, I get a direct connection to the medicares around the country; so those claims and era’s are always direct. I find the Blues are the same way. I’ve always been able to get a direct connection for those as well.
The commercial payers tend to enter contracts with a “preferred clearinghouse” and that company makes money on both sides. The payer pays them and in turn they charge the provider. In cases like this I find the cheapest route to get the claims to the payer.