Ad agencies depend on people working together to create campaigns for their clients. Sometimes there is one leader and the rest are just part of their team. The use of IBM Notes and Domino provide that easy way to manage information and provide access to it from multiple channels.
I know, hard to believe, but this has been the case for most of the 20 years Lotus Notes has been around. Browser, phone, tablet and access across multiple clients of MAC, Linux and Windows. Get out of your shell and live a little.
Prefer Gmail? Great, they are finally getting to understand what companies need from an Enterprise email solution. They will catch up someday, if they stay with it.
Maybe people do not like the UI. I hate Saab's, I think they are ugly cars, but people love them. And that's okay, I have a choice in which car I buy. Do you like the iPhone but only get Android from work? Tough luck, but they pay the bills and in the end it is just a phone with apps and works only as well as your admins let it, or your service provider.
If you view Notes as an email client, you are giving up on the real benefits it provides you on an individual and team basis. Personal databases, while seeming to sound difficult, are really easy to implement and produce a wealth of benefits from saved time to find information, reducing email sizes through using links instead of attachments, security levels which are almost non-existent in Outlook even blog posting and wiki editing offline. For more you can see examples at http://openntf.org.
Does using one email client over another really cause emails to be delayed 2 days? Of course not. Those are server side issues for administrators to manage.
What about the meeting invitations appearing differently? Here's a great question for you, ask your internal email marketing team how many different variations of email/phone/device clients they need to test for before they send a message out. How many do they truly test? Because of changes Microsoft made in how Outlook and Exchange render HTML over the years you would need to test with every version.
It would be nice if all systems were utilitarian and open and not created in such ways to push the boundary of RFC SMTP guidelines but that is another story.