Target pharmacies were bought by CVS. No Walmart in NYC, nor the other chains that you mention. NYC is dominated by Walgreens, Rite Aid, Duane Reade, CVS.
The ability to open a pharmacy in an area isn't restricted the way Internet and television providers are. Nothing stops a new store or chain from opening.
Pharmacies operate in large share through health plans. Larger pharmacies == more negotiating power == higher drugs prices. Smaller / start-up chains don't have that advantage, and hence start with several strikes against them.
This is misleading. Most independent pharmacies operate through coalition or coops in the exact same way small grocery stores do. Often times the sales of coops are on par with, or can easily exceed, the annual sales of major chains.
You aren't going to match Walmart on $4.00 generics and have success, but often times independent chains get better discounts on everything else than many of the major chains.
Except for market saturation. E.g, Walgreens, Duane Reade, and two CVS stores within two or three (short) blocks. Walgreens at 97th & Broadway, Duane Reade at 94th & Broadway, CVS at 93rd & Broadway, CVS at 96th & Amsterdam (which is one block from Broadway).
Aaah, that I did not realize. But still, it seems like there's a fair amount of competition among pharmacies in the general sense. I suppose that in specific geographic locales that may not be as true though.
And I'm not saying that this merger is unilaterally a "Good Thing" or anything. It just doesn't strike me as a place where anti-trust specifically comes into play.