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As you're a new hire and unless you were hired in a marketing/branding position you won't really be qualified to suggest change or have the political capital to push it through. That signature is so far beyond the reasonable that I don't think you'll have much luck openly campaigning for change.

The only reasonable and safe course of action to take in your situation is to lead by example. Convert that entire mess of banners into a single modestly-sized banner. Find the smaller versions of those logos (i.e. the ones actually meant for inclusion in an email) and convert all of them into a single banner image that's no more than few lines high.

Whenever someone notices or comments on your signature, explain that you preferred a more subtle and cleaner look for your signature. With any luck, this will make its way up the management chain and if there are any reasonable managers left they'll then have an alternative design they can use to convince the maniac who standardised this.