The 'suggestion' in this case is a lie. What they mean is 'it'll make it easier for us to get more paying customers in more quickly'.After the performance, we suggest that the doors at the front of the theatre give quicker access to the car park.
In my calmer moments, I have to recognize that people are using 'suggest' in ways like this; it seems to mean 'say, but in as uncontentious a way as possible'. 'I said that it was time to leave' means 'I said "It's time to leave"'; 'I suggested that it was time to leave' seems to mean something like 'I said "Wouldn't you agree that it's time to leave? I don't want to be a party-pooper, but the baby-sitter will charge extra if we get back after midnight".'
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