[exim] Received and Deleting Headers

If I am about to send out an Email that I'm relaying (based on
Authentication), I was thinking that it would be useful to delete the
"Received: " header lines (which in this case, is usually the ISP
connected employee laptop that has just authenticated to me).

Since these headers are 'easily forged' anyway, and since these headers
are sometimes triggers for various remote SPAM scoring tools, I was
thinking that deleting them may be harmless...

1) Why would this be a bad idea? (I'm guessing it is, but I don't know why)

2) Is this even possible - especially if there are multiple 'Received'
lines?

Thanks,
Gary Allen