Let's be frank here for a minute.
The only reason that I use a hardware email client is for the instant search capabilities that I have.
I was an early adopter of gmail and one of my favourite features was the instant search speed of the google servers. When you wanted to find a key word it would look at a huge number of emails instantly and the search provided relevant results too!
When I started using multiple emails on different domains I quickly needed to find an email client to aggregate multiple accounts and gmail didn't seem to fit the bill anymore.
My first problem with using an email client became apparent about 3 or 4 months in. I started to experience a slow lag every time I needed to check my email. I don't like to keep my email client open while I'm working because I find it distracting, and this was in the days before solid state drives!
My new solution is to keep my inbox clear constantly in my email client while keeping my important emails in a folder that isn't my inbox. The Apple Mail client is smart enough to not fetch these messages until I want to browse that folder, so voila, instant inbox almost all the time!