Getting mail of various accounts in the inbox of one account does not work well

When I ask mail of various accounts to arrive all at the inbox of one (main) account, Thunderbird no longer downloads the messages from that main account: It says there are no messages, even if there are. In that case I can only download the messages of that main account if I use the option Download/Sync under the Offline option. The messages of the other accounts DO arrive in the inbox of my main account. I have compared the prefs.jr of the "conflated" version, which does not work, with the version where the other accounts are visible and not associated with the main account