IMO, for the applications the OP lists, cordless drills have compleatly replaced corded drills.
I also agree the OP needs a drill, not an impact driver. I like my impact, but its a specialized tool that really only meets its fully potential in trained hands.
And with how inexpensive the M12 series or similar tools are, there is no reason not to step up to that type of tool, it will last a lot longer.
I have both M12 series tools and NiCad 18V Dewalt tools and I any time I go for the tools there is always at least one battery with enough charge to get me started, at least until the second battery charges (which is only about 30 minutes for the M12). More than enough for the around-the-house jobs. For big jobs, I try to remember to get batteries on the chargers before I start.
I much prefer the fine speed control and automatic stop on most cordless drills. For homeowner applications, they are the way to go.
My corded drill is a 1/2" Bosch hammer-drill, which will get me through everything I do. With the regular chuck I can use it to mix mortar and joint compound, and still drill reasonable size holes in whatever I want. SDS is nice, but again its a specialized thing.