Answer:
Assuming that the LLC is legitimately operating under more than one fictitious name (DBA name), whether a bank will allow the business to use a single account for the multiple businesses is a matter of bank policy. Aside from the differences in service charge income, the principal concern of the bank could be the ability of its systems to display the additional DBA names to tellers (who would depend on the information to know whether checks payable to the individual businesses can be accepted for deposit to the LLC's one account).
If the operational and fee income concerns can be dealt with by the bank and the LLC, there's no reason not to permit it.
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