Increase drain size?

Question

My kitchen sink has a good size drain pipe heading into the basement and out:

And what I assume is a pretty normal connection from the drain to the sink:

But when you look at the drain in the sink, the way it's all put together, the actual holes through which water can drain are quite limited:

I can't help but think that if this were set up better, the sink would drain faster and possibly get clogged less often. Is there a different tailpiece or other part that I can get that has a wider diameter? Or are these so standardized that what I've got is all I can get?

EDIT

I realize my original post didn't really capture my question accurately. So yes, I always have a strainer:

and my question is not about the crossbars in the standard strainer (I've labeled "YES" in the image below), but rather the piping that lies right beneath the strainer and seems to impinge on the drain (labeled "NO" in this image):

EDIT 2

The black "stack" is a 2" pipe at floor level, but it shrinks as it goes up. The white pipe that branches off to the sink is 1 1/2" as suspected:

Answer 1

The sink drain you show in the picture is a standard kitchen drain that meets code. Its only purpose is to drain water. Based on your post it seems that you are getting clogs in your drain at the mouth of the drain as shown in your picture. It may not drain fast enough for you but it is doing what it's designed to do, trap large debris before it passes down the drain resulting in a potentially costly repair. To make the openings any larger could result in a blockage issue.
It's also a good idea to use the strainer that fits in the drain. It's much easier to clean out the strainer than to have to call a plumber.