That was the whole point of the movie. He did not get caught until the end, and so he got the chance to wreck havoc at the party.

It's a damn good comedy, so it cannot be entirely pointless!
"The Opener of the Way is Waiting"

The setup at the beginning is to show that Sellers' character has an unfortunate habit of screwing up - but, given what happens in the pre-credit sequence, it would be inconceivable for him to then be invited to the Clutterbuck's party. Consequently, it is necessary for a plot device to exist to invite him accidentally - that's all there is to it, but it certainly isn't pointless, it is a necessary plot device. Subsequently, the film isn't about Bakshi's relationship with his studio bosses so that aspect of it doesn't need to be explored and it doesn't matter what (if anything) happens when they realise who he is.

To be honest the only pointless thing here seems to be your critique.

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