Forwarding an email does change things like headers etc though doesn't it?
Google's mailbox forwarding isn't like "I'm going to forward this mail to my mom" forwarding. It's essentially a redirection, so yes, the delivery envelope changes, but all of the headers that you the email recipient or sender care about remain intact.
I have a GoogleApps account with a non-profit org I help out with, which is forwarded to my main personal account. My main gmail account is set up to reply to these forwarded emails using the email address the original email was sent to.
I sent an email from my work account (XXXXX.YYYYY@BUSINESS.com) to my non-profit email address (XXXXX@ALTERNATEDOMAIN.COM). Here are the additional headers tacked onto the envelope as it got forwarded to my personal account (XXXXX.YYYYY@gmail.com):
Delivered-To: XXXXX.YYYYY@gmail.com
Received: by 10.28.179.68 with SMTP id c65csp147718wmf;
Fri, 9 Oct 2015 10:58:29 -0700 (PDT)
X-Received: by 10.50.65.100 with SMTP id w4mr615970igs.61.1444413508967;
Fri, 09 Oct 2015 10:58:28 -0700 (PDT)
Return-Path: <XXXXX+caf_=XXXXX.YYYYY=gmail.com@ALTERNATEDOMAIN.COM>
Received: from mail-io0-f179.google.com (mail-io0-f179.google.com. [209.85.223.179])
by mx.google.com with ESMTPS id jf3si1824565igb.26.2015.10.09.10.58.28
for <XXXXX.YYYYY@gmail.com>
(version=TLSv1.2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128);
Fri, 09 Oct 2015 10:58:28 -0700 (PDT)
Received-SPF: neutral (google.com: 209.85.223.179 is neither permitted nor denied by best guess record for domain of XXXXX+caf_=XXXXX.YYYYY=gmail.com@ALTERNATEDOMAIN.COM) client-ip=209.85.223.179;
Authentication-Results: mx.google.com;
spf=neutral (google.com: 209.85.223.179 is neither permitted nor denied by best guess record for domain of XXXXX+caf_=XXXXX.XXXXX=gmail.com@ALTERNATEDOMAIN.COM) smtp.mailfrom=XXXXX+caf_=XXXXX.YYYYY=gmail.com@ALTERNATEDOMAIN.COM
Authentication-Results: spf=none (sender IP is )
smtp.mailfrom=XXXXX.XXXXX@BUSINESS.com;
Received: by mail-io0-f179.google.com with SMTP id 1so86167261iow.1
for <XXXXX.YYYYY@gmail.com>; Fri, 09 Oct 2015 10:58:28 -0700 (PDT)
X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed;
d=1e100.net; s=20130820;
h=x-original-authentication-results:x-gm-message-state:delivered-to
:date:from:to:subject:message-id:mime-version:content-type
:content-disposition:user-agent:spamdiagnosticoutput
:spamdiagnosticmetadata;
bh=/09Z88CogcSnnv6M3ksyjvqSrgQjlNE50KWqH68QaJE=;
b=HYs8SbioT9+pDurQ/RCjkg0ACn9/YdAObA24OJ4zYbIz0aQIYUVfc49eKj7lLT4ojn
ag7ToB8d7FTXackHsfOE0BTvjZnLF85B7h3cjdz37KWKgrdpdA5Lpp4vwoQHftVlcrOg
PkVO0Qcbyr6zMk9ffQm6xyVG1w2BNUXHji7o77O++oOjoOaFfyD+y+AVmsrXQ+vqlXQ0
KxKkSvFfwfgHJdEUD9hSorHl7qBHMoXuB2O7hifFGC+rcPVyYTeryay7bES/rNmKhKQK
uALzfyhM0sKIsizv37qgftQ3f29iCe7kzR3hfQimo+nm1RNJkK+Su+m2GJbpAbteb+4X
T31Q==
X-Original-Authentication-Results: mx.google.com; spf=pass (google.com: domain of XXXXX.YYYYY@BUSINESS.com designates 157.56.111.95 as permitted sender) smtp.mailfrom=XXXXX.YYYYY@BUSINESS.com
X-Gm-Message-State: ALoCoQkTrTiLJqhxI+NmlqHm2QTcisttZqdxcXsQ5S86Fj23Q8kWPaplLTx2yt6fwDVxVrcY73lZ
X-Received: by 10.107.156.14 with SMTP id f14mr16828156ioe.32.1444413508622;
Fri, 09 Oct 2015 10:58:28 -0700 (PDT)
X-Forwarded-To: XXXXX.YYYYY@gmail.com
X-Forwarded-For: XXXXX@ALTERNATIVEDOMAIN.COM XXXXX.YYYYY@gmail.com
To me, it makes no sense to have one gmail account fetch another gmail account's email across POP3. It adds an unnecessary protocol to the mix, and it's one more set of account credentials you have to maintain to keep the system running -- for no real benefit. If you're playing wholly within the Google email ecosystem, it makes more sense to do the forwarding thing, IMO.